CONCRETE 
DESIGNERS'  MANUAL 


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CONCRETE 
DESIGNERS'   MANUAL 


TABLES  AND  DIAGRAMS  FOR  THE  DESIGN 

OF 
REINFORCED  CONCRETE  STRUCTURES 


BY 

GEORGE  A.  HOOL,  S.B. 

CONSULTING    ENGINEER,    PROFESSOR   OF   STRUCTURAL,   ENGINEERING, 
THE   UNIVERSITY   OF   WISCONSIN 


AND 

CHARLES  S.  WHITNEY,  M.C.E. 

STRUCTURAL   ENGINEER  „  MT-    rAUXEEr  WI8. 


FIRST  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC. 

NEW  YORK:    370  SEVENTH  AVENUE 

LONDON:    6  &  8  BOUVERIE  ST.,  E.  C.  4 

1921 


H  k7 


COPYRIGHT,  1921,  BY  THE 
McGRAW-HiLL  BOOK  COMPANY,  INC. 


THE     MAP»L>:     I'KKHS     YORK    PA 


PREFACE 


The  tables  and  diagrams  presented  in  this  manual  make  possible  the  rapid  design- 
ing of  reinforced  concrete  structures  in  accordance  with  the  Joint  Committee  Recom- 
mendations, the  American  Concrete  Institute  Recommendations,  the  New  York 
Building  Code  Requirements  and  the  Chicago  Building  Code  Requirements.  Some 
of  these  tables  and  diagrams  will  also  be  found  of  such  a  general  nature  that  they 
can  be  used  when  the  designing  requirements  are  different  from  any  of  those  men- 
tioned. No  tables  are  presented  based  on  the  flat  slab  recommendations  of  the 
Joint  Committee  as  these  recommendations  are  so  conservative  that  they  are  not 
used  to  any  extent. 

The  authors  have  for  some  time  been  preparing  and  using  in  their  practice  various 
tables  and  diagrams  in  order  to  finally  obtain  complete  data  in  the  most  convenient 
form  and  of  the  greatest  value  to  the  majority  of  designing  engineers.  The  collection 
given  in  this  book  is  the  result. 

No  attempt  has  been  made  to  develop  theory  or  to  duplicate  information  not 
directly  relating  to  concrete  design  which  can  conveniently  be  found  hi  other  hand- 
books possessed  by  all  designers. 

G.  A.  H. 
April,  1921.  C.  S.  W. 


£47789 


CONTENTS 

PAGE 

STANDARD  NOTATION 1 

FORMULAS ........   i.    .  2 

SECTION    1 — SLABS »   .   . .   i   ........  5 

SECTION    2 — FLAT  SLABS i    ......  31 

SECTION    3 — RECTANGULAR  BEAMS 47 

SECTION    4 — DOUBLY  REINFORCED  BEAMS 63 

SECTION    5 — T-BEAMS 77 

SECTION    6 — SHEAR  REINFORCEMENT .  83 

SECTION    7 — COLUMNS. 91 

SECTION    8 — BENDING  AND  DIRECT  STRESS \.    .    .  199 

SECTION    9 — FOOTINGS 225 

SECTION  10 — MISCELLANEOUS . 237 

APPENDIX — RULINGS  PERTAINING  TO  DESIGN  AND  WORKING  STRESSES 243 

Joint  Committee  Recommendations 243 

American  Concrete  Institute  Recommendations 255 

New  York  Building  Code  Requirements 265 

Chicago    Building    Code  Requirements 270 


VU 


CONCRETE 
DESIGNERS1  MANUAL 


FLEXURE  FORMULAS  USED  IN  PREPARING  TABLES  AND  DIAGRAMS 

The  flexure  formulas  made  standard  by  the  Joint  Committee  relate  to  working 
stresses  and  safe  loads,  and  are  based  on  the  straight-line  theory  of  stress  distribution. 
These  formulas  were  used  in  preparing  the  tables  and  diagrams  in  this  book. 

STANDARD  NOTATION 

Rectangular  Beams. 

fs  =  tensile  unit  stress  in  steel. 
fe  =  compressive  unit  stress  in  concrete. 
E»  =  modulus  of  elasticity  of  steel. 
Ee  =  modulus  of  elasticity  of  concrete. 
H. 

n  =  Fc 

M  —  moment  of  resistance,  or  bending  moment  in  general. 
As  =  steel  area. 

b  =  breadth  of  beam. 

d  =  depth  of  beam  to  center  of  steel. 

k  =  ratio  of  depth  of  neutral  axis  to  depth  d. 

z  =  depth  below  top  to  resultant  of  the  compressive  stresses. 

j  =  ratio  of  lever  arm  of  resisting  couple  to  depth  d. 

jd  =  d  —  z  =  arm  of  resisting  couple. 

^ 
p  =  steel  ratio  =  7-3- 

T-Beams. 

b  =  width  of  flange. 
b'  =  width  of  stem. 
?  =  thickness  of  flange. 
Beams  Reinforced  for  Compression. 
A'  =  area  of  compressive  steel. 
p'  =  steel  ratio  for  compressive  steel. 
//  =  compressive  unit  stress  in  steel. 
C  =  total  compressive  stress  in  concrete. 
C"  =  total  compressive  stress  in  steel. 
d'  =  depth  to  center  of  compressive  steel. 
z  =  depth  to  resultant  of  C  and  C'. 
Shear,  Bond  and  Web  Reinforcement, 
r  =  total  shear. 

V  =  total  shear  producing  stress  in  reinforcement. 
v  =  shearing  unit  stress. 

fo  1 


*  TORMULAS 


u  =  bGiid^tres^pef  >unii  area  of  :bar. 
o  =  circumference  or  perimeter  of  bar. 
So  =  sum  of  the  perimeters  of  all  bars. 
T  =  total  stress  in  single  reinforcing  member. 
s  =  Horizontal  spacing  of  reinforcing  members. 

Av  =  area  of  shear  steel  in  section  of  beam  considered  (A.  C.  I.  notation). 
fv  —  tensile  stress  in  web  reinforcement  (A.  C.  I.  notation). 
a  =  spacing  of  shear  steel  measured  perpendicular  to  its  direction  (A.  C.  I. 

notation). 
Columns. 

A  =  total  net  area. 
As  =  area  of  longitudinal  steel. 
Ac  =  area  of  concrete. 
P  =  total  safe  load. 

FORMULAS 
Rectangular  Beams. 

k  =  V2pn  +  (pnT*  -pn  =  -  I—  =  - 


or  -,     or 

jr.-ar.yCW,   or   w-^.-   or  f 

_  2fsp  f.k 

'~ 


n(l  -  k) 

T-Beams.  —  With  a  T-beam  it  is  necessary  to  distinguish  two  cases;  namely,  (1) 
the  neutral  axis  in  the  flange,  and  (2)  the  neutral  axis  in  the  web. 

Case  /.  The  Neutral  Axis  in  the  Flange.  —  All  formulas  for  "moment  calculations" 
of  rectangular  beams  apply  to  this  case.     It  should  be  remembered,  however,  that 
b  of  the  formulas  denotes  flange  width,  not  web  width,  and  p  (the  steel  ratio)  is 
A,       x  A, 
W  not  Vd 

Case  II.  The  Neutral  Axis  in  the  Web.  —  The  amount  of  compression  in  the  web 
is  commonly  small  compared  with  that  in  the  flange,  and  is  generally  neglected.  The 
formulas  to  use,  assuming  a  straight-line  variation  of  stress  and  neglecting  the  com- 
pression in  the  web,  are: 

1 


k  = 


i+4 

nfe 

2ndAs  +  btz 
2nAa  +  2bt 


=  3kd  -  2t    t_ 
2kd  -    t'3 
jd  =  d  -  2 

2 


FORMULAS 


M         M 

J°       A,jd      pjbd* 

fe  =  n(l  -  fc) 
-V 


•  "  ft 

,  =  f,Ajd 


Approximate  formulas  can  also  be  obtained.  The  arm  of  the  resisting  couple  is 
never  as  small  as  d  —  %t,  and  the  average  unit  compressive  stress  is  never  as  small 
as  K/c,  except  when  the  neutral  axis  is  at  the  top  of  the  web.  Using  these  limiting 
values  as  approximations  for  the  true  ones, 

Mc  =  V2fcbt(d  -  i#) 

M,  =  AJ.(d  -  HO,  or  At  =    - 


The  errors  involved  in  these  approximations  are  on  the  side  of  safety. 

Formulas  which  take  into  account  the  compression  in  the  stem  are  recommended 
.where  the  flange  is  small  compared  to  the  stem.  Such  formulas  may  be  found  in  the 
report  of  the  Joint  Committee,  and  are  as  follows  : 


pnd 

\- 


A,  +  (6  -  b')t*   .    fnA.  +  (b  -  b')i\  *      nA,  +  (b  -  b')t 


[(kd  - 


t(2kd  -  l)b  +  (kd  -  t)*b' 
jd  =  d  -  z 

fa  =-**- 

.        2Mkd 

[(2kd  -  t)bt  +  (kd  -  t)*b']jd 

Rectangular  Beams  Reinforced  for  Compression. 


p'        +  n*(p  +  p';2  -  n(p 


,         M          M 

Js 


Ajd      pjbd* 

f  f'k 

n(l  -  fc) 

>--*THi 


FORMULAS 

fen(l  -  k) 

k 
Ms  =  bd%pj 


Shear,  Bond  and  Web  Reinforcement. 

V 


Joint  Committee  (Recommended  V  = 
Vertical  web  reinforcement 

Tjd 

-- 


'    s  /    \ 

=  -vj-  (a) 

Bars  bent  up  at  angles  between  20  and  45  deg.  with  the  horizontal, 
and  web  members  inclined  at  45  deg. 

_  Asfgjd  _     Tjd  V^s 

~  0.75F'  ~  0.75F'  4  jd 

American  Concrete  Institute: 

Avfvjd  _  V'a 

o,  —  — TTT —  or  Av 
V 


Columns. 

Square  Cored 

P  =  Afdl  +  (n  -  l)p] 
Round  Cored  Hooped 

P  =  Afe[l  +  (n  -  l)p] Joint  Committee 

P  =  Afe[(l  +  4np')  +  (n  -  l)p] Am.  Cone.  Inst. 

P  =  Afe[l  +  (n  -  l)p]  +  2/sp'A New  York  Code 

P  =  Afe(l  +  2.5wp')[l  +  (n  -  Dp! Chicago  Code 

(In  the  above  formulas  pf  =  percentage  of  spiral.    /,  in  the  New  York 
formula  is  taken  at  20,000  Ib.  per  sq.  in.) 


SECTION  1 
SLABS 

Diagrams  1  to  9  inclusive  give  the  total  safe  loads  on  solid  slabs  of  different  depths 
for  the  various  combinations  of  working  stresses,  bending  moment  coefficients  and 
span  lengths. 

Diagrams  10  and  11  give  the  bending  moments  for  different  values  of  the  total  load 
per  square  foot,  the  span  length,  and  the  bending  moment  coefficients. 

Diagrams  12  to  17  inclusive  may  be  used  to  find  the  moments  of  resistance  and 
area  of  steel  required  in  solid  slabs  for  various  combinations  of  working  stresses. 

Table  1  may  be  employed  to  find  the  size  and  spacing  of  round  or  square  rods  for  a 
given  sectional  area  of  steel  per  foot  of  solid  slab. 

Tables  2  to  7  inclusive  give  the  total  safe  load  for  ribbed  slabs  for  various  combinations 
of  working  stresses. 

Example  of  Design  of  Solid  Slab 

Given:  Live  load  =  300  Ib.  per  sq.  ft.;  span  length  =  8  ft.  6  in.;  M  =  ~;  jc  =  650; 

/.  =  16,000;  n  =  15. 

Using  Diagram  3,  a  slab  of  8%-H.  span,  with  a  depth  to  steel  of  4%  in.,  is  found 
to  have  sufficient  strength  to  carry  a  total  load  of  405  Ib.  per  sq.  ft.  Assuming  a 
5>9-in.  rough  slab  with  1  in.  of  finish  on  top  (not  placed  monolithically)  and  plastered 
below,  the  loading  will  be  as  follows : 

6^  in.  of  concrete  =81 

Plaster =     5 

Live  load =300 

Total  load  =386  Ib.  per  sq.  ft. 
Diagram  11  shows  the  bending  moment  for  this  load  on  an  8 3^ -ft.  span,  when 

rty«/2 

M   =  12-,  to  be  27,900  in.-lb 

Entering  Diagram  12  at  the  left  with  this  bending  moment,  it  is  found  that  the 
area  of  steel  required  per  foot  width  for  a  slab  having  a  depth  to  steel  of  4%  in.  is 
0.42  sq.  in.,  or  K-in.  round  rods  spaced  5^  in.  on  centers  (see  also  Table  1). 

The  use  of  the  bending  moment  coefficient  ^2  means  that  the  slab  is  continuous 
over  supports  and  that  the  area  of  steel  over  the  supports  must  be  the  same  as  at  the 
center  of  the  span.  From  Diagram  25,  page  57,  it  will  be  found  that  one-half  of  the 
rods  can  be  bent  up  from  the  bottom  at  22  in.  from  the  support  and  these  rods  should  be 
run  to  the  quarter  point  of  the  adjacent  span. 

Example  of  Design  of  Ribbed  Slab 

Given:  Live  load  =  100  Ib.  per  sq.ft.;  hottow-tile  floor;  span  of  joists  —  19  ft;  M  = 
~;fc  =  650;  /.  =  16,000;  n  =  15. 

5 


SLABS 

Assuming  a  2-in.  topping  and  an  8-in.  tile,  Table  2  shows  the  total  safe  load  to  be 
190  lb.  per  sq.  ft.,  with  a  steel  area  per  joist  of  0.90  sq.  in.  The  table  also  shows  the 
dead  weight  of  floor  to  be  73  lb.  per  sq.  ft.  which  makes  a  total  load  to  be  carried  of 
173  lb.  per  sq.  ft.,  or  less  than  the  maximum  safe  load.  The  floor  is  usually  plastered 
below,  which  would  make  the  total  load  178  lb.  per  sq.  ft.  A  3)4- in.  topping  with  6-in. 
tile  would  also  answer. 

When  the  size  of  tile  and  thickness  of  topping  have  been  determined,  it  is  necessary 
to  design  the  joists  with  reference  to  shear,  bond,  and  compression  in  the  concrete  at 
the  haunch  by  treating  them  as  individual  beams. 


DIAGRAM  1 


SOLID 
SLABS 


SAFE  LOAD  ON  SOLID  CONCRETE  SLABS 

IT/2 


M 


8 


fc=650 
fs  =  16,000 
fs  =  18,000 
n=15 


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SOLID 
SLABS 


DIAGRAM  2 


fs=16,000 
fs=  18,000 


SAFE  LOAD  ON  SOLID  CONCRETE  SLABS 

"5 


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DIAGRAM   11 


SOLID 
SLABS 


BENDING  MCMENt- 'FOR  SLABS   •  :;': 


SOLID 
SLABS 


DIAGRAM  12 


fc  =650  MOMEOT  *  OP  kfcSlSTAWCE  AttD  STEEL  REQUIRED 

fs=16,000  FOR 

n=15  SOLID  CONCRETE  SLABS 


Area  of  steel  in  sq.  in.  per  ft  width 


DIAGRAM   13 


SOLID 
SLABS 


MOMENT  OF  RESIST  AN  CE>  AiNLX  ST-EET^ -RfcQtf  H£ED  fc=650 

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Area  of  steel  in  sq.  m.  per  ft  width  or  s  ab 


SOLID 
SLABS 


DIAGRAM  14 


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fa=16,000 

n=15 


AND  STEEL  REQUIRED 
'1 
SOLID  CONCRETE  SLABS 


Area  of  steel  in  sain,  per  ft  width  of  felab 


DIAGRAM   15 


SOLID 
SLABS 


MOMENT  OF  RESISTANCE  AND  3TELT,.  REQUEUED 
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n  =  15 


Area  of  steel  in  sq.  in.  per  ft  width  of  slab 


SOLID 
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DIAGRAM  16 


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fs=16,0 
n=15 


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SOLID  CONCRETE  SLABS 


Area  of  steel  in  sq.in.perft.widthof  slab 


22 


DIAGRAM  17 


SOLID 
SLABS 


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FOR  f.  =  18,C 

SOLID  CONCRETE  SLABS  n  =  15 


Area  of  steel  in  sa  in,  oer  ft.  width  o 


SOLID 
SLABS 


TABLE  1 


SPACING  OF  RODS  IN  SLABS 


ROUND  RODS 

Diam- 
eter 
(inches) 

Sectional  area  of  steel  per  foot  of  slab  when  spaced  as  follows: 

2  in. 

2Y2  in. 

3  in. 

3^  in. 

4  in. 

4^  in. 

5  in. 

5H  in. 

6  in. 

7  in. 

Sin. 

9  in. 

10  in. 

12  in. 

K 

Ke 

H 

Ke 
H 

Me 

*A 
1X< 
% 
l*A* 
H 
We 
1 

1  H 
i  H 
i  « 
i  M 

0.29 
0.46 
0.66 
0.90 

0.23 
0.36 
0.53 
0.72 
0.94 

0.20 
0.31 
0.44 
0.60 
0.78 
0.99 

0.17 
0.26 
0.38 
0.51 
0.67 
0.85 

0.15 
0.23 
0.33 
0.45 
0.59 
0.75 
0.92 

0.13 
0.20 
0.29 
0.40 
0.52 
0.66 
0.82 
0.99 

0.12 
0.18 
0.26 
0.36 
0.47 
0.60 
0.74 
0.89 

0.17 
0.24 
0.33 
0.43 
0.54 
0.67 
0.81 
0.96 

0.15 
0.22 
0.30 
0.39 
0.50 
0.61 
0.74 
0.88 

0.13 
0.19 
0.26 
0.34 
0.43 
0.53 
0.64 
0.76 
0.89 

0.17 
0.23 
0.29 
0.37 
0.46 
0.56 
0.66 
0.78 
0.90 

0.15 
0.20 
0.26 
0.33 
0.41 
0.49 
0.59 
0.69 
0.80 
0.92 

0.13 
0.18 
0.24 
0.30 
0.37 
0.45 
0.53 
0.62 
0.72 
0.83 
0.94 

0.15 
0.20 
0.25 
0.31 
0.37 
0.44 
0.52 
0.60 
0.69 
0.78 
0.99 
1.23 
1.48 
,.77 

1.18 

1.49 
1.84 

1.19 
1.47 
1.78 

1.23 
1.48 
1.77 

1.05 
1.27 
1.51 

1.78 

2.23! 
2.65 
3.11 
3.61 

1.11 
1.32 
1.56 

1.80 

2.12 
2.48 
2.88 
3.31 
3.77 

1.18 
1.38 
1.60 

1.84 

1.06 
1.24 
1.44 
1.66 

1.88 

2.07 
2.40 
2.76 
3.14 
3.98 

1.13 
1.31 
1.51 
1.71 

.04 
.20 
.38 

.57 
.99 

2.06 
2.37 
2.69 
3.41 

1.03 
1.18 
1.35 
1.70 

4.14 
4.71 

2.07 
2.36 
2.98 
3.68 

1.03" 
1.18 
1.49 
1.84 
2.23 
2.65 

2.09 
2.65 
3.27 
3.96 

1.05 
1.33 
1.64 
1.98 

4.77 

2.39 
2.95 
3.56 

2.17 
2.68 
3.24 
3.86 

1.19 
1.47 

1.78 

4.91 

4.21 

2.45 
2.97 
3.53 

2.10 

2:55 

3.03 

5.09 

4.45 
5.30 



4.71 

4.24 

2.36 

2.12 

SQUARE  RODS 

Di- 
men- 
sion 
(inches) 

Sectional  area  of  steel  per  foot  of  slab  when  spaced  as  follows: 

2  in. 

2M  in. 

3  in. 

3H  in. 

4  in. 

4M  in. 

5  in. 

5H  in. 

6  in. 

7  in. 

8  in. 

9  in. 

10  in. 

12  in. 

K 

-«6 

^ 
Me 
K 
Ke 
^ 
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% 
l«6 

% 
% 

1 

i  H 
i  K 

1    ^8 
1    H 

0.37 
0.59 

0.84 

Iti6 

1.50 
1.90 

0.30 
0.47 
0.67 
0.92 

0.25 
0.39 
0.56 

0.77 

0.21 
0.33 
0.48 
0.66 

0.86 

0.19 
0.29 
0.42 
0.57 
0.75 
0.95 

0.17 
0.26 
0.37 
0.51 
0.67 
0.84 

0.15 
0.23 
0.34 
0.46 
0.60 
0.76 

0.13 
0.21 
0.31 
0.42 
0.55 
0.69 

0.12 
0.19 
0.28 
0.38 
0.50 
0.63 

0.17 
0.24 
0.33 
0.43 
0.54 

0.15 
0.21 
0.29 
0.37 
0.47 

0.13 
0.19 
0.25 
0.33 

0.42 

0.17 
0.23 
0.30 
0.38 

0.14 
0.19 
0.25 
0.32 

1.20 
1.52 

1.00 
1.27 

1.08 

2.34 
2.84 
3.37 
3.96 

1.87 

1.56 
1.99 

1.34 
1.62 
1.93 

1.17 
'1.42 
1.69 
1.98 

1.04 
1.33 
1.50 
1.76 

0.94 

0.85 

0.78 
0.94 

0.67 
0.81 
0.96 

0.59 
0.71 
0.84 
0.99 

0.52 
0.66 
0.75 

0.88 

0.47 
0.57 
0.67 
0.79 
0.92 

0.39 
0.47 
0.56 
0.66 
0.77 
0.88 

2.27 
2.70 
3.17 
3.67 

1.13 
1.35 
1.58 

1.84 

1.03 
1.23 

1.44 
.1.67 
1.92 

2.25 
2.64 
3.06 
3.52 

1.12 
1.32 
1.53 
1.76 

2.26 
2.62 
3.01 
3.43 
4.34 
5.36 
6.48 

1.13 
1.31 
1.51 
1.71 

4.59 
5.27 
6.00 

2.30 
2.64 
3.00 
3.80 

2.04 
2.34 
2.67 
3.37 

1.15 
1.32 
1.50 

1.89 

l.t)2 
1.17 
1.33 
1.69 

4.22 
4.80 
6.08 

2.11 
2.40 
3.04 
3.75 

1.05 
1.20 
1.52 

1.87 

4.00 
5.06 
6.25 

2.18 
2.76 
3.41 

2.00 
2.53 
3.12 

3.78 

1.00 
1.27 
1.56 
1.89 

2.17 
2.68 
3.24 

3.86 

4.69 
5.67 
6.75 

4.17 
5.04 
6.00 

2.34 
2.84 
3.37 

2.08 
2.52 
3.00 

....      .... 

4.54 
5.40 

4.12 
4.91 

2.27 
2.70 

4.50 

2.25 

TABLE  2 


RIBBED 
SLABS 


SAFE  LOAD  OH  RIBBED  SLASS  :    : 


c  =  650 
fs=16,000 
n=15 


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TABLE  3 


: :  SAFE-  LOAD-  ON  MBBED  SLABS 


fc—700 
f.  =16,000 


8 

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TABLE  4 


SAFE  LOAD  ON 
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0  b-  CO 


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CS  X  O  <N  O  O  CO 


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the  distance  center  to  center  of  joists  and  divid 
the  distance  center  to  center  of  joists  and  divid 


cs  ic  i-t  i>     O<NOO»C^N.CO     w  w  •*  o  b-  co  cs 

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ing  of  joists  multiply  the  values  in  these  columns 
ing  of  joists  multiply  the  values  in  these  columns 


For  other 
For  other 


27 


RIBBED 
SLABS 


TABLE  5 


v..  j»t  <  SAfcE  JLQ&P,  k)N  RIBBED  SLABS 


fs=  18, 


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28 


TABLE  6 


RIBBED 
SLABS 


SAFE  LOAD  ON  *IBBEJ>  SLABS 

fc=700 
f,  =  18,000 


oad. 


Total  safe  load  in  pounds  per  square  foot 
including  weight  of  floor  (dead  and  live) 

on  M  -  ~~  For  M  -  ~.  add  20%  to 


!    g 


rH  TO  •<!•  1C  TO  TO  X 
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16. 
24. 


ter  of  joists  and  divid 
ter  of  joists  and  divid 


ce  center  to 
ce  center  to 


the  d 
the  d 


mns 
mns 


col 


er  spacing  of  joists  multiply  the  values  in  these 
er  spacing  of  joists  multiply  the  values  in  these 


oth 


For 
For 


29 


RIBBED 
SLABS 


TABLE  7 


LPADPJJF  RIBBED  SLABS 
'  fc  =  750  ' 


24." 


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SECTION  2 
FLAT  SLABS 

The  designs  of  square  interior  flat  slab  panels  according  to  the  American  Concrete 
Institute  recommendations,  and  the  New  York  and  Chicago  Codes  are  given  in  Tables 
8  to  13  inclusive.  These  are  for  panels  from  16  to  26  ft.  square,  both  with  and  without 
drops,  and  for  live  loads  from  100  to  350  Ib.  per  sq.  ft.  of  floor.  An  allowance  of  6  Ib. 
per  sq.  ft.  was  made  for  weight  of  finish. 

The  quantities  given  are  believed  to  be  conservative  and  by  careful  detailing  it  will 
usually  be  found  possible  to  keep  the  weight  of  the  steel  slightly  below  that  given  in 
the  tables. 

Rectangular  panels  and  wall  panels  must  be  designed  according  to  the  special 
requirements  of  the  different  codes. 

Columns  supporting  flat  slab  floors  must  be  designed  to  take  the  bending  moments 
produced  by  the  cantilever  action  of  the  slab.  After  the  bending  moments  in  the 
columns  have  been  estimated,  the  stresses  may  be  determined  by  the  diagrams  of 
Section  8.  The  majority  of  columns  used  have  round  hooped  cores  and  Diagrams  60 
to  64  inclusive  have  been  constructed  for  the  design  of  such  columns  when  subjected 
to  bending. 


31 


FLAT 
SLABS 


FLAT  SLAB  FLOORS 

AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS 
INTERIOR  SQUARE  PANELS 

fc=650  for  positive  moment 
fc=750  for  negative  moment 
f3=  16,000 


JL 


!?> 

« :jo         ' 

*>!§       ^ 
!a        \ 

—I J- 


T\  w; 

LM- 


•a 


*:0> 

^f 


i         *|^0  »;0^  I 

t — ab. ^jv] — «j-. 


iQ 


.^J — 

> 


+ 

i 


i^n 


-J. 


\ 


l^;|i 

;gfi 
•§i^^ 


tii 


-j (Vj 

Aj 


-s\j 


a: 


JSP 

? 


•IS 


S)i 


*  231 

SI 

/" 


' lltll !       Drop  Construction       j '  Cap  Construction 


h 


Section    A-A 


Bending  Moment  Coefficients 

Moment  coefficients  shown  on  diagram  are  to  be  multiplied  by  WL. 
W  =  wL\ 

w  =  total  dead  and  live  load  in  pounds  per  square  foot. 
L  =  span  center  to  center  of  columns  for  square  panels. 
Values  shown  above  moment  coefficients  are  percentages  of  numerical  sum  of  moments  in  one 

direction  across  panel. 

Numerical  sum  of  moments  in  one  direction  across  panel  =  0.0648  WL. 
Minimum  size  of  drop  =0.3L. 
Minimum  diameter  of  capital  =  0.225L. 

,,.  .  [  0.02L\/w  +  1  (t  in  inches,  L  in  feet) 

Minimum  t  = 


t  =  total  thickness  of  slab. 


32 


TABLE  8 

FLAT  SLAB  FLOORS 

AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS 
INTERIOR  SQUARE  PANELS 

DROP  CONSTRUCTION 

fc  =  650  for  positive  moment 
fc  =  750  for  negative  moment 
f, 
n=15 


FLAT 
SLABS 


Superimposed  load  =  100  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
ttiam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

4'  10"  X  4'  10" 

6 

2K 

0.52 

14-%" 

8-% 

H-% 

1.95 

17X17 

3'  9" 

5'    2*X5'    2" 

6j-£ 

2J4 

0.56 

16-%" 

9-% 

13-% 

2.14 

18X18 

4'  0" 

5'    6"X5'    6" 

6^i 

ovz 

0.58 

18   %" 

10-% 

15  % 

2.25 

19X19 
20X20 

4'  3" 
4'  6" 

5'    8"X5'    8" 
6'    0"X6'    0" 

?i 

iM 

0.62 
0.65 

21-%" 
17-Ke" 

11-% 

16-% 

15   K   * 

2.38 
2.53 

21  X21 

4'  9" 

6'    4"X6'    4" 

8 

25^ 

0.69 

20-Ke* 

10  -K 

16-K   * 

2.70 

22X22 

5'  0" 

6'    8"X6'    8" 

O  I/ 

0.71 

21  -He* 

12-H 

16-K    * 

2.81 

23X23 
24X24 

5'  3" 
5'  6" 

7'    0"X7'    0" 
7'    4"X7'    4" 

9^ 

3M 

0.76 
0.78 

23-Ke" 
26-K6* 

13-K 

14-  K 

18-K   * 
21-K  * 

3.06 
•      3  .  30 

25X25 

5'  9" 

7'    6"X7'    6" 

9K 

3J£ 

0.82 

29-K6* 

16-K 

23—  K   * 

3.44 

26X26 

6'0" 

7'  10"  X  7'  10"          9% 

3^ 

0.84        31-Ke*      17-K 

25-K   * 

3.55 

Superimposed  load  =  150  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

4'  10"  X  4'  10" 

6 

2%               0.52 

18-%" 

10-%" 

15-% 

2.54 

17X17 

3'  9" 

5'    2"X5'    2" 

6J^ 

234               0.56 

20-%" 

16-% 

2.56 

18X  18 

4'  0" 

5'    6"X5'    6" 

gax 

3K               0.59 

23-%" 

14-%" 

19   % 

2.90 

19X19 

4'  3" 

5'    8"X5'    8" 

7H 

0.63 

26-%" 

14-%" 

20-% 

3.00 

20X20 
21X21 

4'  6" 
4'  9" 

6'    0"X6'    0" 
6'    4*X6'    4" 

J* 

3H 
3M 

0.65 
0.69 

22-Ke"      12-He* 
24-Ke"      13-He* 

17-K 
20   K 

3.27 
3.52 

22X22 

5'  0" 

6'    8*X6'    8" 

8J<4 

4 

0.72 

26-K6* 

14-Ke" 

22   K 

3.62 

23X23 

5'  3" 

7'    0"X7'    0" 

8^i 

4 

0.76 

29  -He* 

16-He* 

23-K 

3.78 

24X24 

5'  6" 

7'    4"X7'    4" 

& 

0.78 

31-Ke' 

18-He* 

26-K 

3.98 

25X25 

5'  9" 

7'    6"X7'    6" 

9M 

4j| 

0.83 

35  Ke" 

29-  K 

4.27 

26X26 

6'0" 

7'  10"  X  7'  10" 

9*i 

4%              0.85 

39-Ke* 

21-He* 

31-K 

4.45 

Superimposed  load  =  200  Ib.  per  sq.  ft. 

• 

Round  steel  rods  in  each  band 

Panel 
size 
(feet) 

Capital 
diam- 
eter. 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 
17X17 

3'  6" 

3'  9* 

4'  10"  X  4'  10" 
5'    2"X5'    2" 

i 

3 

0.58 
0.59 

20-% 

24-% 

11-%" 
13-%" 

17-%" 
19-%" 

2.83 
3.07 

18X18 

4'  0* 

5'    6"X5'    6" 

7J4 

3?i 

0.63 

26-% 

15-%" 

22-%" 

3.45 

19  X  19 

4'  3" 

5'    8"X5'    8" 

7H 

4 

0.66 

30-% 

16-%" 

25-%" 

3.50 

20X20 

4'  6" 

6'    0"X6'    0" 

8 

4 

0.70 

25-  K   * 

13-Ke* 

20-Ke* 

3.70 

21X21 
22X22 

4'  9" 
5'0" 

6'    4"X6'    4" 
6'    8"X6'    8" 

m 

A  1  ^ 

0.72 
0.76 

27-  K    * 
30  -H   * 

16-Ke* 

22-Ke" 
25-K  6* 

3.87 
4.15 

23X23 

5'  3" 

V    0"X7'    0" 

9  J4 

4-  ^> 

0.81 

33-  K   * 

18-He* 

26-K.6" 

4.26 

24X24 

5'  6" 

V    4"X7'    4" 

9M 

5 

0.83 

36-K   * 

20-K6* 

30-Ke" 

4.45 

25X25 
26X26 

5'  9"  . 
6'  0" 

7'    6"X7'    6* 
7'  10"  X  7'  10" 

10 

5 

0.87 
0.92 

39  -He" 
43-K6* 

22-Ke* 
23-Ke* 

31-He* 

4.59 
4.92 

33 


FLAT 
SLABS 


TABLE  8 

FLAT  SLAB  FLOORS 

AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS 
INTERIOR  SQUARE  PANELS 

DROP  CONSTRUCTION 

fc  =  €50  for  positive  moment 
fc  =  750  for  negative  moment 
fs=  16,000 
n=15 


Superimposed  load  =  250  Ib.  per  sq.  ft. 

Round  steel  rods  in  each  band 

Panel 

size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

4'  10"  X  4'  10" 

7 

3K 

0.61 

22-%" 

12-%" 

18-% 

3.05 

17X17 

3'  9" 

5'    2"X5'    2" 

7M 

3^ 

0.65 

25-%" 

14-%" 

20   % 

3.32 

18X18 

4'0" 

5'    6"X5'    6" 

4 

0.68 

28-%" 

17-%" 

23    % 

3.55 

19X19 

4'  3" 

5'    8"X5'    8" 

SjJ-i" 

0.72 

23-  KG" 

20-  K 

3.77 

20X20 

4'  6" 

6'    0"X6'    0" 

8H 

4H 

0.74 

27-  fi6" 

14-Kc" 

22-K 

4.00 

21X21 
22X22 

4'  9" 
5'0* 

6'    4"X6'    4" 
6'    8"X6'    8" 

9 

4% 

0.79 
0.83 

30-K6" 
33-Me" 

16-Ko" 
18-Kc" 

23-  K 
26-K 

4.15 

4.42 

23X23 

5'  S" 

7'    0"X7'    0" 

10 

5 

0.87 

35-Kc" 

20-Kc" 

29    K 

4.60 

24X24 

5'  6" 

7'    4"X7'    4" 

5 

0.91 

39-Kc" 

22-Kc" 

31-K 

4.81 

25X25 

5'  9" 

7'    6"X7'    6" 

11 

5/4 

0.96 

43-Kc" 

23-Kc" 

36-K 

5.21 

26X26 

6'0" 

7'  10"  X  7'  10" 

UK 

5% 

0.98 

47-Kc" 

26-K  6  " 

38-K 

5.39 

Superimposed  load  =  300  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

4'  10"  X  4'  10" 

7K 

3% 

0.66 

25-%" 

14-%" 

19-%" 

3.35 

17X17 

3'  9" 

5'    2"X5'    2" 

7% 

4  1/ 

0.68 

29-%" 

16-%" 

23-%" 

3.70 

18X18 

4'  0" 

5'    6"  X  5'    6" 

4% 

0.72 

31-%" 

18-%" 

25-%" 

3.83 

19X19 

4'  3" 

5'    8"X5'    8" 

8% 

434 

0.77 

14-Kc" 

21-Kc 

4.07 

20X20 

4'  6" 

6'    0"X6'    0" 

9M 

4% 

0.81 

29  ^KG" 

16  KG" 

23-  KG 

4.30 

21X21 

4'  9" 

6'    4"X6'    4" 

9% 

5 

0.85 

3  1  -  K  G  " 

26-  KG 

4.47 

22X22 

5'  0" 

6'    8"X6'    8" 

10 

0.88 

35-Kc" 

20-Kc" 

29-  K  e 

4.82 

23X23 

5'  3" 

7'    0"X7/    0" 

10H 

5% 

0.92 

3  6-  KG 

21-Kc" 

30-  KG 

4.77 

24X24 

5'  6" 

7'    4"X7'    4" 

11 

6M 

0.96 

18-  M" 

26-  Yz" 

5.25 

25X25 

5'  9" 

7'    6"X7'    6" 

i  iM 

6M 

1.01 

35-^  " 

20—  Yv  " 

29  -K" 

5.52 

26X26 

6'0" 

7'  10"  X  7'  10" 

12 

7 

1.05 

39-  W* 

22-M" 

5.77 

Superimposed  load  =  350  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

4'  10"  X  4'  10" 

7% 

4% 

0.68 

27-%" 

14-%"         23   %" 

3.79 

17X17 

3'  9" 

5'    2"X5'    2" 

8  z4 

5 

0.73 

30   %" 

16-%" 

25-%" 

3.91 

18X18 

4'  0" 

5'    6"X5'    6" 

8% 

5M 

0.77 

26-Kc 

20-Kc" 

4.10 

19X19 

4'  3" 

5'    8"X5'    8" 

5% 

0.82 

27-  KG 

14-Kc" 

22-Ke* 

4.27 

20X20 

4'  6" 

6'    0"X6'    0" 

9% 

6 

0.86 

17-K6" 

25  KG" 

4.55 

21X21 

4'  9" 

6'    4"X6'    4" 

10J4 

6J4 

0.90 

34-  KG 

18-Kc" 

4.81 

22X22 

5'  0" 

6'    8"X6'    8" 

10% 

6% 

0.95 

36-K  6 

30-K6" 

4.96 

23X23 

5'  3" 

7'    0"X7'    0" 

\\YL 

0.99 

40-  KG 

23—  KG" 

33-KK" 

5.26 

24X24 

5'  6" 

7'    4"X7'    4" 

11% 

7% 

1.04 

34-  M" 

19-M"        28-^" 

5.54 

25X25 

5'  9" 

7'    6"X7'    6" 

1.09 

37—  M" 

2\-Yz"        30-  K" 

5.76 

26X26 

6'0" 

7'  10"  X  r  10" 

12% 

8H 

1.13 

41-K" 

33-M" 

6.07 

34 


TABLE  9 

FLAT  SLAB  FLOORS 

AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS 
INTERIOR  SQUARE  PANELS 

CAP  CONSTRUCTION 

fc  =  650  for  positive  moment 
fe  =  750  for  negative  moment 
fs  =  16,000 
n=15 


FLAT 
SLABS 


Superimposed  load  =  100  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 

diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 

Across 

Diagonal 

each  way 

16X16 

3'  6* 

6M 

0.542 

17-%* 

4-%* 

Q  a/  it 

13-%* 

2.54 

17X17 

3'  9* 

Q^A, 

0  .  563 

20-%* 

4-%* 

n-%" 

15-%* 

2.66 

18X18 

4'  0* 

7 

0.584 

23   %* 

e     3  /  tt 

12-%* 

2.84 

19X19 

4'  3* 

7^4 

0.625 

25-%* 

5-%* 

13-  %* 

19-%* 

3.04 

20X20 
21X21 

4'  6* 
4'  9* 

8 

0.667 
0.688 

24-Ke" 

4  Ke*. 

11-Ke" 

16-Ke" 
18-Ke" 

3.24 
3.45 

22X22 

5'0* 

8% 

0.730 

26-Ke" 

5  Ke* 

14-Ke" 

19-Ke" 

3.62 

23X23 
24X24 

5'  3* 
5'  6* 

9 

0.750 
0.792 

29  7^e* 
32-Ke" 

4-Ke* 

15-7^6* 
17-Ke* 

23-Ke* 

3.78 
3.96 

25X25 

5'  9* 

9?i 

0.813 

35-Ke" 

5—  Ke* 

18-Ke" 

26-Ke" 

4.17 

26X26 

6'0* 

10 

0.833 

39-Ke* 

5—  Ke 

21-Ke* 

29-Ke"           4.36 

Superimposed  load  =  150  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 

sq.  ft. 

Direct 

Direct  over 
column,  add'l 

Across 

Diagonal 

each  way 

16X16 

3'  6 

7 

0.583 

20-%* 

4-%* 

n-%* 

14-%* 

2.83 

17X17 

3'  9 

0.605 

23-%* 

4-%* 

12  %* 

17_i^» 

2.98 

18X18 

4'  0 

7% 

0.646 

26-%* 

4—%* 

14-%* 

19  %* 

3.14 

19X19 

4'  3 

8M 

0.688 

21   Ke 

4-Ke" 

12-Ke" 

15-Ke* 

3.27 

20X20 
21X21 
22X22 

4'  6 
4'  9 
5'  0 

0  I/ 

9 

Ql/ 

0.709 
0.750 
0.792 

mi 

29-  K  e 

4-Ke" 
6-Ke" 
5-Ke" 

13-Ke" 
15-Ke" 
16-Ke" 

18-Ke" 
20-Ke" 
21-Ke* 

3.48 
3.78 
3.91 

23X23 
24X24 
25X25 
26X26 

•5'  3 
5'  6 
5'  9 
6'0* 

Q3X 

IOH 
11 

0.813 
0  .  854 
0.875 
0.917 

32-  K  e 
35-Ke 
39-Ke 
42-Ke 

5-Ke" 
6-Ke" 
5   Ke" 
6  Ke" 

18  Ke* 
19-Ke* 
21-Ke" 
24-Ke" 

24  -Ke" 
26-Ke* 
28-Ke" 
31-Ke* 

4.16 
4.34 
4.51 
4.76 

Superimposed  load  =  200  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 
each  way 

Across 
direct 

Diagonal 

16X16 
17X17 

3'  6* 
3'  9* 

JM 

0.625 
0.667 

22-%*     1          5-%* 
25   %*               5-%* 

12   %* 

14-%* 

19-%* 

3.12 
3.29 

18X18 

4'  0* 

8^£ 

0.708          29-%*              5-%* 

16-%* 

21-%* 

3.49 

19X19 

4'  3* 

9 

0.750          23   Ke 

5-Ke"               13-Kfi* 

17-Ke" 

3.66 

20X20 
21X21 

4'  6* 
4'  9* 

10  2 

0.791          26  Ke 
0.833          29-Ke 

4-Ke" 
5-Ke* 

14-Ke" 
16-Ke" 

19-Ke" 
21-Ke" 

3.88 
4.04 

22X22 

5'0* 

10^ 

0.875     !     32-Ke 

4-Ke" 

17-Ke" 

23-Ke* 

4.20 

23X23 

5'  3* 

\\y\ 

0.938          34-Ke 

5-Ke* 

19  Ke" 

25-Ke" 

4.37 

24X24 

5'  6* 

12                    1.000     j     SS-Tie 

4-Ke" 

21-Ke" 

28-7^6* 

4.64 

25X25 

5'  9* 

12%               1.063          41-Ke 

4~Ke* 

23-Ke* 

4.78 

26X26            6'0*               13J4               1.142          47~Ke     i         5-Ke"              26  Ke"        34  -Ke"          5.23 

35 


FLAT 
SLABS 


TABLE  9 

FLAT  SLAB  FLOORS 

AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS 
INTERIOR  SQUARE  PANELS 

CAP  CONSTRUCTION 

fc=650  for  positive  moment 
fc=750  for  negative  moment 
fs  =  16,000 
n  =  15 


Superimposed  load  =  250  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 

sq.  ft. 

Direct 

Direct  over 
column,  add'l 
each  way 

Across 
direct 

Diagonal 

16X16 

3'  6" 

8% 

0.730 

21-% 

6-%" 

n-%" 

16-%" 

3.00 

17X17 

3'  9" 

0.771 

26-% 

4-%" 

14   %" 

19—%" 

3   30 

18X18 

4/0" 

10 

0.833 

29-% 

4-%" 

16-%" 

23-%" 

3.61 

19X19 
20X20 

4'  3" 
4'  6" 

}°?| 

0.896 
0.959 

23-  H   " 

26  -H   " 

4-He" 
4-He" 

13-Ke" 
15-He" 

17-  He" 
19   He" 

3.64 
3.91 

21X21 
22X22 
23X23 
24X24 
25X25 
26X26 

4/  9// 
5'  0" 
5'  3" 
5'  6" 
5'  9" 
6'  0" 

12 
13 

15g4 

.000 
.083 
.146 
.188 
.250 
.313 

28-He" 
31-He" 
34-He" 
38-He" 
41  -He" 
45-Ke* 

2-Ke" 
4-He" 
5-He" 
4-He^ 

4-He" 

15-  He" 
17-He" 
19-He" 
21    He" 
23-He" 
25-He" 

20-He" 
23   He" 
25-He" 
28-He" 
30-He" 
33-He" 

3.84 
4.16 
4.37 
4.65 
4.81 
5.03 

Superimposed  load  =  300  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct  over 
Direct         column,  add'l 
each  way 

Across 
direct 

Diagonal 

! 

16X16 

3'  6" 

10 

0.833 

23-%" 

3-%"                  13-%" 

17-%" 

3.17 

17X17 

3'  9" 

10% 

0.896 

26-%" 

2-%"                  14-%" 

19-%" 

3.27 

18X18 

4'  0" 

11  J^ 

0.958 

29-%" 

3-%" 

16-%" 

21    %" 

3   45 

19X19 

4'  3" 

12M 

.042 

32-%" 

2-%" 

23-%" 

3.58 

20X20 
21X21 

4/  6" 
4'  9'^ 

13 

14 

.083 
.174 

27   He" 
29   He" 

3-He" 
3   He" 

15-He" 
16-He" 

19-  He" 

21-He" 

3.88 
4.02    . 

22X22 
23X23 

5'0" 
5'  3" 

15 
16 

.250 
.333 

32-  He" 
34   He" 

2-He" 
4-He" 

IB-He" 
19  He" 

23-  He" 
25-He" 

4.20 
4.33 

24X24 
25X25 
26X26 

5'  6" 
5'  9" 
6'Q" 

17  2 
18 

.375 
.417 
.500 

38-He" 
42-He" 
46-He" 

3  He" 

21-He" 
24  -He" 
25-He" 

28-He" 
31-He" 
30-He" 

4.64 
4.76 
4.84 

Superimposed  load  =  350  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 
each  way 

Across 
direct 

Diagonal 

16X16             3'  6" 

HM 

0.958 

23-%" 

2-%" 

13-%" 

•  17  %" 

3.16 

17X17     !       3'  9" 

12K 

1.021 

26-%" 

2-%" 

14-%" 

19-%" 

3.23 

18X18            4'  0" 

13 

1.083 

29   %" 

3   %" 

16-%" 

21-%" 

3.45 

19X19            4'  3" 

13% 

1.146 

33    %" 

3-%" 

18-%" 

24-%" 

3.74 

20X20 
21X21 
22X22 
23X23 
24X24 

4'  6" 
4'  9" 
5'  0" 
5'  3" 
5'  6"  - 

14% 
15% 
16% 
17% 
18% 

1.230 
1.313 
1.396 
1.480 
1.563 

27-He" 
29-He" 
32-He" 
35-He" 
37-He" 

2-He" 
3-He" 
-  3-He 

HK 

3-  He 

14^He" 

18~8f6" 
20-He" 
21-He" 

19-He" 
21-  He" 
23-He" 
26-He" 
27-He" 

3.85 
4.02 
4.22 
4.48 
4.50 

25X25 

5'  9" 

19% 

1.646 

41-He" 

30-He" 

4.79 

26X26 

6'0" 

20% 

1.730 

45-He" 

3-Ke" 

25-He" 

33-Ke" 

5.00 

36 


FLAT  SLAB  FLOORS 

NEW  YORK  CITY  BUILDING  CODE 

INTERIOR  SQUARE  PANELS 

fc=650  for  positive  moment 
fc=750  for  negative  moment 
ft  =  16,000 


FLAT 
SLABS 


Bending  Moment  Coefficients 

Moment  coefficients  shown  on  diagram  are  to  be  multiplied  by  WL. 
W  =  wL* 

w  =  total  dead  and  live  load  in  pounds  per  square  foot. 
L  =  span  center  to  center  of  columns  for  square  panels,  or  average  span  for  rectangular 

panels  where  long  dimension  is  not  more  than  1.1  times  short  dimension. 
Values  shown  above  coefficients  are  percentages  of  numerical  sum  of  moments  in  one  direction 

across  panel. 

Numerical  sum  of  moments  in  one  direction  across  panel  =  0.0587TFL. 
Minimum  size  of  drop  =  0.33L. 
Minimum  diameter  of  capital  =  0.225L. 
'6 

0.02L\/wJ_+  1  with  drop 
0.024L\/w  +  IK  without  drop 
L/32 
t  =  total  thickness  of  slab. 


Minimum  t  = 


(t  in  inches,  L  in  feet) 


37 


FLAT 
SLABS 


TABLE  10 


FLAT  SLAB  FLOORS 

NEW  YORK  CITY  BUILDING  CODE 

INTERIOR  SQUARE  PANELS 

DROP  CONSTRUCTION 

fc  =  650  for  positive  moment 
fc=750  for  negative  moment 
ft  =16, 000 
n=15 


Superimposed  load  =  100  Ib.  per  sq.  ft. 

Panel 

size 
(feet) 

Capital 
diameter 

Size  of 
drop 
panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

1 
Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across' 
direct 

Diagonal 

i 

16X16 

3'  6" 

5'  4" 

6 

3 

0.528 

13-% 

9-% 

9-%" 

1.76 

17X17 

3'  9" 

5'  8" 

3 

0.570 

15-% 

10-%" 

1.89 

18X18 

4'  0" 

6'  0" 

6% 

334 

0.593 

17-% 

12-% 

12-%" 

2.04 

19X19 

4'  3'" 

6'  4" 

734 

33^2 

0.636 

19-% 

14-% 

13-%" 

2.14 

20X20 

4'  6" 

6'  8" 

7^| 

3% 

0.660 

21-% 

16-% 

15-%" 

2.30 

21X21 

4'  9" 

7'0" 

8 

4 

0.704 

23  -% 

17-%" 

17-%" 

2.40 

22X22 

5'  0'' 

7'  4" 

4 

0.725 

26-% 

19   %" 

19-%" 

2.57 

23X23 
24X24 

5'  3" 
5'  6" 

7'  8" 
8'0" 

8% 

*H 

'   0.770 
0.794 

22-Ke" 
24-Ke" 

16-Ke" 

16-Ke" 
17-Ke" 

2.85 
2.95 

25X25 

5'  9" 

8'  4" 

9^<2 

*H 

0.835 

26-Ke"      19-Ke* 

3.10 

26X26 

6'0" 

8'  8" 

9% 

5 

0  .  858 

29-Ke"      21-Ke" 

21-Ke" 

3.30 

Superimposed  load  =  150  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diameter 

Size  of 
drop 
panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

5'  4" 

6 

3 

0.528 

16-% 

12-% 

12-%" 

2.24 

17X17 

3'  9" 

5'  8" 

63-4 

334 

0.571 

18-% 

13-% 

13-%" 

2.32 

18X18 

4'  0" 

6'  0" 

6% 

0  .  595 

20-% 

15-% 

15-%" 

2.48 

19X19 

4'  3" 

6'  4" 

734 

4 

0.641 

22-% 

17-% 

16-%" 

2.54 

20X20 

4'  6" 

6'  8" 

7^| 

4 

0.662 

25-% 

19-% 

19-%" 

2.62 

21X21 

4'  9" 

7'  0" 

8 

434 

0.706 

27-% 

20   % 

20   %" 

2.82 

22X22 

5'0" 

7'  4" 

SM 

0.727 

23  Ke" 

17-Ke" 

3.15 

23X23 

5'  3" 

7'  8" 

4% 

0.774 

25   Ke" 

19   Ke" 

18-Ke" 

3.24 

24X24 

5'  6" 

8'  0" 

934 

5 

0.817 

27—  Ke" 

20-Ke" 

20-Ke" 

3.36 

25  X  25 
26X26 

5'  9" 
6'  0" 

8'  4" 
8'  8" 

10 

0.841 

0.887 

30-Ke'' 
32-Ke" 

22-K6" 
24-Ke" 

22-Ke" 
24-Ke" 

3.58 
3.72 

Superimposed  load  =  200  Ib.  per  sq.  ft. 

j 

~                   Round  steel  rods  in  each  band 

Panel 
size 

(feet) 

Capital 
diameter 

Size  of 
drop 
panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

5'  4" 

6H 

334 

0.571 

18-%" 

13-%" 

13-%" 

2.46 

17X17 

3'  9" 

5'  8" 

7 

0.618 

20   %" 

15   %" 

14-%" 

2.54 

18X18 

4'  0" 

6'  0" 

734 

434 

0.643 

22-%" 

17-%" 

16-%" 

2.67 

19X19 

4'  3" 

6'  4" 

434 

0.685 

24-%" 

18-%" 

18-%" 

2.80 

20X20 
21X21 

4'  6" 
4'  9" 

6'  8" 
7'  0" 

gg 

JM 

0.729 
0.775 

20-Ke" 

15-Ke" 

15   Ke" 
16-Ke" 

3.04 
3.14 

22X22 

5'  0" 

7'  4" 

9 

O  '4. 

0.799 

25-Ke" 

ig_7^6" 

18-Ke" 

3.38 

23X23 

5'  3' 

7'  8" 

93^ 

5H 

0.841 

27-Ke" 

21-Ke" 

20-Ke" 

3.54 

24X24 
25X25 

5'  6" 
5'  9" 

8'  0" 
8'  4" 

10 

$ 

0.887 
0.954 

31-  Ke" 

22-Ke" 
24-Ke" 

23-Ke" 

3  .  66 
3.77 

26X26 

6'0" 

8'  8" 

1  1  34 

GH 

1.002 

34-Ke" 

26-Ke" 

25-Ke" 

3  .  94 

: 

38 


TABLE  10 


FLAT  SLAB  FLOORS 

NEW  YORK  CITY  BUILDING  CODE 

INTERIOR  SQUARE  PANELS 

DROP  CONSTRUCTION 

fe=650  for  positive  moment 
fe  =750  for  negative  moment 
fs=16,000 


FLAT 
SLABS 


Superimposed  load  =  250  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diameter 

Size  of 
drop 
panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16             3'  6 

5'  4* 

7M 

4 

0.662 

17-%; 

13-%* 

13-%* 

2.39 

17X17            3'  9 

5'  8* 

8 

4% 

0.706 

15-%* 

15-%' 

2.62 

18X18     i       4'  0 
19X19            4'  3 

6'  0' 
6'  4* 

8* 

4% 

0.752 
0.797 

22-%* 
25-%* 

17-%* 
19   %\ 

17—%* 
18-%* 

2.76 
2.87 

20  X  20            4'  6 

6'  8* 

9% 

5 

0.859 

21-^6" 

15-Ke*. 

3.11 

21X21 

4'  9 

7'  0* 

10% 

0.906 

23-He" 

17   Ke". 

3.29 

22X22 

5'0* 

7'  4* 

10% 

6 

0.953 

25-Ke" 

18—  M« 

3.38 

23X23 

5'  3* 

7'  8* 

HM 

6 

1.014 

27-He" 

20-^g* 

20-He 

3.51 

24X24 

5'  6* 

8'  0* 

12 

6H 

1.060 

30-He* 

22   He". 

22-^6 

3.71 

25X25 
26X26 

5'  9* 
6'0* 

8'  4* 
8'  8* 

12%               7% 

13%       m 

1.129 
1.215 

32-^6* 
27-M" 

19-^* 

3.80 
3.98 

Superimposed  load  =  300  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diameter 

Size  of 
drop 
panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 
17X17 

3'  6* 
3'  9* 

5'  4* 
5'  8* 

8j* 

J* 

0.749 
0.796 

20-%* 

i3-%: 

13-%* 
15-%* 

2.46 
2.62 

18X18 

4'  0* 

6'  0* 

9% 

5 

0.858 

22-%* 

17-%* 

16-%* 

2.67 

19X19 

4'  3" 

6'  4* 

5% 

0.928 

25-%* 

19-%\ 

1?-^"/, 

2.87 

20X20 

4'  6* 

6'  8* 

lit! 

6% 

0.996 

20-Ke" 

3.04 

21X21 

4'  9* 

7'  0* 

n% 

6% 

1.043 

22-Ke* 

17-K6" 

16  -He* 

3.14 

22X22 

5'  0* 

7'  4* 

12  J^ 

6% 

1.104 

25-He" 

18—  T^R* 

18-Ke" 

3.36 

23X23 
24X24 

5'  3* 
5'  6* 

7'  8* 
8'  0* 

13% 
13% 

7% 
7  V*> 

1.169 
1.215 

27-Ke* 
30-He* 

20-^6* 
22-He* 

20-K6*. 

3.51 
3.71 

25X25 

5'  9* 

8'  4* 

14^£ 

8 

1.283 

32-Ke* 

24-K6* 

23—  J^  «* 

3.80 

26X26 

6'0* 

8'  8* 

i«S 

9 

1.375 

19-8* 

19-M* 

3.90 

Superimposed  load  =  350  Ib.  per  sq.  ft. 

Panel 
size 

(feet) 

Capital 
diameter 

Size  of 
drop 
panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic' 
feet  per 
sq.ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

i 

| 

16X16 

3'  6* 

5'  4* 

9^               5 

0.827 

18-%* 

13-%* 

13-%*     !       2.46 

17X17 

3'  9* 

5'  8* 

10                    5% 

0.882 

21-%* 

15-%* 

15-%*            2.68 

18X18 

4'  0*              6'  0* 

10%               6 

0.951 

23-%' 

17  %; 

16-%*            2.74 

19X19 

4'  3*              6'  4* 

11  4                6% 

.017 

26-%* 

18-%*^   i       2.90 

20X20 

4'  6*              6'  8* 

.101 

21-He*. 

1  5-  K  6  * 

21X21 

4'  9*              7'  0*       i     13%               7% 

.169 

17—  "^i  e* 

16-Ke*          3^21 

22X22 

5'  0*              7'  4*             14                   7% 

.239 

25-lil" 

19-Ke* 

IS-Mo"          3.38 

23X23 

5'  3*               7'  8*             15                   8 

.324 

28-K6* 

20   Ke* 

24X24 

5'  6*               8'  0*             15%               8% 

.393 

22-  He* 

21—  7A*," 

3.64 

25X25 

5'  9*               8'  4* 

16%               9%                .483        32-T<«" 

24-Ke* 

23—  TY«* 

3.80 

26X26 

6'  0*              8'  8* 

17%              9% 

.569        27-H* 

20-M* 

19-M" 

3.98 

39 


FLAT 
SLABS 


FLAT  SLAB  FLOORS 

NEW  YORK  CITY  BUILDING  CODE 

INTERIOR  SQUARE  PANELS 

CAP  CONSTRUCTION 

fc=650  for  positive  moment 
fc=750  for  negative  moment 
f,  =16,000 
n  =  15 


Superimposed  load  =  100  Ib.  per  sq.  ft. 

Round  steel  rods  in  each  band 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 

sq.  ft. 

Direct 

Direct  over 
column,  add'l 
each  way 

Across 
direct 

Diagonal 

16X16 

3'  6" 

W 

0.562 

14-% 

8-% 

8-%" 

8-%" 

1.91 

17X17 
18X18 

4'0" 

^ 

0.605 
0.645 

18-% 

10-% 

n-% 

10-%" 

9  %" 
10-%" 

2.04 
2.14 

19X19 

4'  3" 

8 

0.667 

21-% 

n-% 

12-%" 

12-%" 

2.34 

20X20 

4'  6" 

8K 

0.708 

23-% 

13-% 

13-%" 

13-%" 

2.44 

21X21 
22X22 
23X23 

4'  9" 
5'  0" 
5'  3" 

9 

9K 

10 

0.750 
0.791 
0.833 

19-K 
21-K 

24-K 

IO-K 

12-K 

11-Ke" 
12-K  e  " 
13-Ke" 

11-Ke" 
12-Ke" 
13-Ke" 

2.66 
2.78 
2.95 

24X24 

5'  6" 

IOK 

0.875 

26-K 

15-Ke" 

14-K  e" 

3.08 

25X25 

5'  9" 

11 

0.917 

29-K 

15-K 

16-Ke" 

15-K  e" 

3.22 

26X26 

0.937 

32-K 

16-K 

18-Ke" 

18-Ke" 

3.56 

Superimposed  load  =150  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab, 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 
each  way 

Across 
direct 

Diagonal 

16X16 

3'  6* 

7% 

0.645 

16-%" 

8-%" 

9-% 

9-%" 

2.12 

17X17 

3'  9" 

S^A 

0.687 

18-%" 

10   %" 

10-% 

10-%" 

2.25 

18X18 

4'0" 

O  1  * 

0.708 

21-%" 

n-%" 

12-% 

12-%" 

2.48 

19X19 

4'  3" 

9 

0.750 

24-%" 

13-%" 

13   % 

13-%" 

2.62 

20X20 

4'  6" 

9K 

0.792 

20-Ke" 

10-Ke" 

11-K   " 

11-Ke" 

2.85 

21X21 

4'  9" 

10 

0.833 

22-Ke" 

12—  K  e" 

12-K    " 

12-K  e" 

2.99 

22X22 
23X23 

5'  0" 
5'  3" 

11 

0.875 
0.917 

25-Ke" 
27-Ke" 

15-Ke" 

14-K    " 

15-K  " 

13  K6" 
14-K  e  " 

3.20 
3.30 

24X24 

5'  6" 

UK 

0.958 

23-K" 

13   K 

3.60 

25X25 

5'  9" 

12 

1.000 

26-K" 

12-K" 

14-K"            3.78 

26X26 

6'0" 

12K 

1.042 

14-K" 

15-K 

15-K" 

3.93 

Superimposed  load  =  200  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 

Across 

Diagonal 

each  way 

16X16 

3'  6" 

8^ 

0.687 

18-%" 

10-% 

10-%" 

10-%" 

2.39 

17X17 

3'  9" 

8% 

0.729 

21-%" 

11-% 

12   %" 

11-%" 

2.55 

18X18 
19X19 

4'0" 
4'  3" 

IH 

0.771 
0.812 

18-Ke" 
19-K  e" 

10-K  " 
ii-K  " 

IO-K  e" 
ll-K  e" 

9-Ke" 
11-K  e" 

2.72 
2.96 

20X20 

4'  6" 

IOK 

0.855 

22-Ke" 

12-K  " 

12-Ke" 

12-K  e  " 

3.27 

21X21 
22X22 

4'  9" 
5'0" 

10££ 

UK 

0.896 
0.958 

25-Ke" 
21-K" 

13-K    " 

\£&' 

13-Ke" 
11   K" 

3.34 
3.52 

23X23 

5'  3" 

12 

1.000 

23-K" 

12-K 

13_^» 

12-K" 

3.61 

24X24 

5'  6" 

12K 

1.042 

25—  K" 

13-K 

14-K" 

3.90 

25X25 
26X26 

5'  9" 
6'  0" 

13 

1.083 
1.145 

QO  I/  '  * 

30-K" 

16-K 

15-K" 
17-K" 

15-K" 

16-K" 

4.09 
4.25 

40 


TABLE  11 


FLAT  SLAB  FLOORS 

NEW  YORK  CITY  BUILDING  CODE 

INTERIOR  SQUARE  PANELS 

CAP  CONSTRUCTION 

fc=650  for  positive  moment 
fe=750  for  negative  moment 
f,=16, 
n=15 


FLAT 
SLABS 


Superimposed  load  =  250  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 

diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 

Across 
direct 

Diagonal 

*    1 

each  way 

16X16      i       3'  6" 

9 

0.750 

19-%" 

10-%" 

11-H" 

n-%" 

2.53 

17X17     i       3'  9* 

9^ 

0.791 

17—^6* 

9—  ^«"               9~J^e" 

9—  'T  i  R  " 

2.75 

18X18            4'  0* 

10 

0.833 

19—  M  6* 

10-Ke*           11-K«" 

10-J^e" 

3.01 

19X19     1       4'  3* 

0.875 

21-Jl  6* 

12-Ke* 

i2-Kfr 

3.21 

20X20 

4'  6" 

11% 

0.937 

23—  Ms* 

12—  1A  e" 

13-K«" 

3.32 

21X21 

4'  9* 

11% 

0.979 

20-}^" 

11-^"              11-^|" 

ii-%" 

3.57 

22X22 

5'0" 

12M 

.042 

oo  \& 

12—  J^"               12—^6" 

12—  J^" 

3.74 

23X23 

5'  3* 

13% 

.104 

24-y2 

13—  V^"          !     13—  J^" 

13-^" 

3.87 

24X24 

5'  6* 

14 

.167 

13-^"          I     15-J^" 

1  5-J4  " 

4.08 

25X25 

5'  9* 

14% 

.229 

29-^ 

14—  M"               16—  J-£* 

16-H* 

4.27 

26X26 

15% 

.292 

14-K" 

17-K' 

4.36 

Superimposed  load  =  300  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Direct  over 
column,  add'l 

each  way 

direct      j 

16X16 

3'  6" 

10% 

0.854 

19-%* 

10-%" 

11-%* 

11-%* 

2.53 

17X17 

3'  9* 

11 

0.917 

17-He* 

8—  J^  «" 

9—  J*f  e* 

9—  M  e* 

2.81 

18X18 

4'0* 

0.958 

Q-T^g" 

10-J^6* 

10-Ke* 

2.95 

19X19 

4'  3* 

12% 

.021 

21—  J^  e* 

H~J^6* 

12-Ke* 

3.12 

20X20 

4'  6* 

13 

.083 

23—  %K" 

H-Ke* 

13—  J^e" 

3.29 

21X21 

4'  9" 

13%                 .  146 

20-^ 

11—  Jl 

11-M" 

3.55 

22X22 

5'  0* 

14^                  .208 

22—  % 

11—  £•£" 

12—  J^ 

12—  i^ 

3.69 

23X23 

5'  3* 

15%                 .271 

24—  i^ 

12—  W" 

14—  J^ 

13—  J-^ 

3.87 

24X24 

5'  6* 

16                      .333 

27~M 

13-^" 

15-M 

14~M 

4;07 

25X25 

5'  9* 

17                     .417 

29-H 

lg_i,^ 

Ig—i^, 

4.22 

26X26 

6'0" 

18                      .500 

its- 

17-M" 

17-H 

4.36 

Superimposed  load  =  350  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 

sq.  ft. 

Direct 

Direct  over 
column,  add'l 
each  way 

Across 
direct 

Diagonal 

16X16 
17X17 

3'  6* 
3'  9" 

12% 

0.958 
1.021 

83f- 

9~/8 

n:?|;. 

11-%"             2.58 
9-Jie*          2.81 

18X18 

4'0" 

13 

1.083 

19-  JH* 

9-He" 

10-Jie" 

10-H«"          2.95 

19X19 

4'  3* 

13% 

1.146 

10—  Ji  e* 

12—  J^e* 

12  Ke"          3.18 

20X20 

4'  6* 

14% 

1.229 

23—  IA  R" 

11—  Me* 

13—  J^is" 

13-Ke"          3.29 

21X21 

4'  9* 

15^ 

1T292 

20-M* 

9—  .H 

n-H 

11-M*            3.52 

22X22 

5'  0* 

16^ 

1.375 

22-K* 

10—  V£ 

12—  J^ 

12->i"            3.69 

23X23 

5'  3* 

17% 

1.437 

11—  i^ 

14_i^ 

13-M" 

3.84 

24X24 

5'  6* 

18% 

1.521 

27-M" 

12-M 

15—  J-^ 

4.11 

25  X  25 

5'  9* 

1.604 

29-M" 

16—  H 

16-1^" 

4.22 

26X26 

6'0" 

20 

1.667           32-M* 

14->r 

17-K 

17-M" 

4.41 

41 


FLAT 
SLABS 


FLAT  SLAB  FLOORS 
CHICAGO  BUILDING  CODE 
INTERIOR  SQUARE  PANELS 


fc  =  700  for  positive  moment 
fc=805  for  negative  moment 
fs=18,000 


.--4- 


&m 
l^p 


-+ 
i 


^dT\  i 


#;vo 

5i   ^ 


^4. 


wj 


Drop  Conatuction 


X 
-J— D! 


<Q 


a. 


ft 

^i  l 


•q 


;iN 

^4-'x/ 

T  Cap  Construction 


?«r^ri/^  R» 
U> 

Section  on  C-C 


^•-•••••••••^ 


Bending  Moment  Coefficients 

Moment  coefficients  shown  on  diagram  are  to  be  multiplied  by  WL. 
W  =  wL* 

w  =  total  dead  and  live  load  in  pounds  per  square  foot. 
L  =  span  center  to  center  of  columns  for  square  panels,  or  average  span  for  rectangular 

panels  where  long  dimension  is  not  more  than  1.05  times  short  dimension. 
Values  shown  above  moment  coefficients  are  percentages  of  numerical  sum  of  moments  in  one 

direction  across  panel. 

Numerical  sum  of  moments  in  one  direction  across  panel: 
for  drop  construction     O.OS25TFL 
for  cap  construction       0.0679 WL 
Minimum  size  of  drop  =  \%L 
Minimum  diameter  of  capital  =  0.225L 

(6 

Minimum  t  =    j  VW/44 

lL/32 

t  =  total  thickness  of  slab. 
t  is  in  inches,  L  is  in  feet. 


42 


TABLE  12 


FLAT  SLAB  FLOORS 
CHICAGO  BUILDING  CODE 
INTERIOR  SQUARE  PANELS 

DROP  CONSTRUCTION 

fe  =  700  for  positive  moment 
fe=805  for  negative  moment 
fs  =18,000 
n  =  15 


FLAT 
SLABS 


Superimposed  load  =  100  Ib.  per  sq.  ft. 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Sise  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6* 

5'  4*X5'4* 

6 

3M 

0.54 

13-%* 

Q  a/ 

10-% 

1.83 

17X17 

3'  9* 

5'8*X5'8* 

3$i 

0.58 

15   %* 

10—% 

11    % 

1.94 

18X18 

4'0* 

6'  0*  X  6'  0* 

6?4               411 

0.60 

H-% 

12   % 

2.04 

19X19 

4'  3* 

6'  4*X6'  4* 

7J4               4  \s± 

0.65 

19-%* 

13-% 

14—% 

2.19 

20X20 
21X21 

4'  6* 
4'  9* 

6'  8*  X  6'  8* 
7'0*X7'0* 

8  *               4X. 

0.67 
0.72 

22-%* 
24-%* 

14-% 
16-% 

16-%        !       2.35 
17   %        !       2.45 

22X22 

5'  0* 

7'  4*X7'  4* 

5 

0.74 

27-%* 

18-% 

19-% 

2.63 

23X23 

5'  3* 

7'  8*X7'8* 

8^i 

51-4 

0.78 

22-Ke* 

14—  Ke" 

16-K   * 

2.81 

24X24 

5'  6* 

8'  0*X8'  0* 

9  /               5H 

0.81 

25-  K  6* 

16-K  e* 

17-K    " 

2.99 

25X25 
26X26 

5'  9* 
6'0* 

8'4*X8'4* 
8'  8*X8'8* 

6 
6 

0.85 
0.87 

27-Ke* 
30-Ke* 

%-%l"' 

18-K   * 
21-Ke" 

3.04 
3.33 

Superimposed  load  ««  150  Ib.  per  sq.  ft. 

Panel 

size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6* 

5'4*X5'4* 

6 

*y* 

0.54 

17-% 

n-% 

12-% 

2.31 

17X17 

3'  9* 

5'8*X5'8* 

6K 

3% 

0.58 

19-% 

13  % 

14-% 

2.46 

18X18 

4'0* 

6'  0*  X  6'  0* 

4 

0.61 

21-% 

15-% 

16-% 

2.63 

19X19 

4'  3* 

6'  4*X6'  4* 

7j^ 

0.65 

25-% 

17-% 

18   % 

2.84 

20X20 

4'  6* 

6'  8*  X  6'  8* 

71,4 

4% 

0.67 

27-% 

18-% 

20-% 

2.95 

21X21 

4'  9* 

7'0*X7'0* 

8 

5 

0.72 

30-% 

20-% 

22-% 

3.09 

22X22 

5'  0* 

7'4*X7'4* 

0.74 

25-Ke* 

16  —  y\ 

17-K  6 

3.23 

23X23 

5'  3* 

7'  8*X7'8* 

8^|               5$i 

0.79 

17-K 

18-Ke 

3.33 

24X24 

5'  6* 

8'  0*X8'  0* 

9                   5%              0.81 

30-Ke* 

20-K 

21-Ke 

3.56 

25X25 

5'  9* 

8'4*X8'4* 

9K               6                  0.85 

34-Ke* 

22  -K 

23-Ke 

3.83 

26X26 

6'0* 

8'8*X8'8* 

10                   6                  0.89 

36-Ke* 

24-K 

25-K. 

3.94 

Superimposed  load  =  200  Ib.  per  sq.  ft. 

Panel 

size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 

(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

1     direct 

Diagonal 

16X16 

3'  6 

5'4*X5'  4* 

6J4 

3H 

0.56     j  21-% 

13-%* 

14-%* 

2.74 

17X17 

3'  9 

5'  8*X5'8* 

6^ 

o  *x 

0  .  58        24-% 

16-%* 

17-%* 

3.01 

18X18 

4'  0 

6'  0*  X  6'  0* 

7 

4^i 

0.62        27-% 

18-%* 

20-%* 

3.25 

19X19 

4'  3 

6'4*X6'4* 

7J4 

4L£ 

0.67 

31-% 

21-%* 

22-%* 

3.47 

20X20 

4'  6 

6'  8*  X  6'  8* 

8 

4£i 

0.72 

24-K 

17-Ke 

18-Ke* 

3.52 

21X21 

4'  9 

7'  0*  X  7'  0* 

8J^ 

5J4 

0.76 

26-K 

18-Ke" 

3.54 

22X22 

5'0 

7'4*X7'4* 

9 

5^| 

0.80 

28-K 

18-Ke 

20-K  e" 

3.66 

23X23 

5'  3 

7'  8*X7'8* 

9J^ 

6 

0.85 

30-K 

20-K  6 

21-Ke* 

3.71 

24X24 

5'  6 

8'0'XS'O* 

10 

0.89 

34-K 

22-Ke 

24-K  e* 

4.03 

25X25 
26X26 

5'  9* 
6'  0* 

8'4*X8'4* 
8'  8*X8'  8* 

11 

i 

0.94 
0.98 

37-K 
39-  K 

24-K  6 
28-K« 

25-Ke* 
29-Ke* 

4.13 
4.39 

43 


FLAT 
SLABS 


TABLE  12 


FLAT  SLAB  FLOORS 
CHICAGO  BUILDING  CODE 
INTERIOR  SQUARE  PANELS 


DROP  CONSTRUCTION 

fe=700  for  positive  moment 
fe=805  for  negative  moment 
fs=18,000 
n=15 


Superimposed  load  =  250  Ib.  per  sq.  ft. 

Round  steel  rods  in  each  band 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 

(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

5'  4"X5'  4" 

6% 

4K 

0.60 

23-%" 

14-%" 

16-%" 

3.03 

17X17 

3'  9" 

5'  8"  X  5'  8" 

7  1/: 

4/4 

0.65 

24-%" 

17-%" 

18-%" 

3.12- 

18X  18 

4'  0" 

6'  0"  X  6'  0" 

73i 

431 

0.69 

27-%" 

18-%" 

19-%" 

3.21 

19X19 

4'  3" 

6'  4"  X  6'  4" 

8J4 

5M 

0.74 

30-%" 

20-%" 

21-%" 

3.33 

20X20 
21X21 
22X22 
23X23 
24X24 

4'  6" 
4'  9" 
5'  0" 
5'  3" 
5'  6" 

6   8"  X  6'  8" 
7'  0"  X  7'  0" 
7'  4"  X  7'  4" 
7'  8"  X  7'  8" 
8'  0"  X  8'  0" 

8M 

10>| 

5/"4 

5* 

88' 

0.78 
0.82 
0.87 
0.92 
0.96 

Al 
8$j 

37-Ke* 

18  -He" 
20-Ke" 
22-Ke" 
24-Ke" 

18-Ke* 
20-Ke" 

24l# 

3.63 
3.77 
3.91 
4.16 
4.31 

25X25 
26X26 

5'  9" 
6'0" 

8'  4"X8'  4" 
8'  8"X8'  8" 

12 

7*4 

7M 

1.03 
1.08 

39-He" 
42-Ke* 

25-Ke" 
28-Ke" 

30-Ke" 

4.41 
4.63 

Superimposed  load  =  300  Ib.  per  sq.  ft. 

Round  steel  rods  in  each  band 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

5'  4"X5'  4" 

7X 

4M 

0.65 

24-%" 

16-%" 

17-%" 

3.20 

17X17 

3'  9" 

5'  8"  X  5'  8" 

8 

4% 

0.72 

27-%" 

17-%" 

18-%" 

3.28 

18X18 

4'  0" 

6'  0"  X  6'  0" 

si* 

0.77 

21-Ke" 

14-Ke" 

3.49 

19X19 

4'  3" 

6'  4"X6'4" 

9 

5/-^ 

0.81 

24-Ke" 

16-Ke" 

17—  H  e" 

3.66 

20X20 

4'  6" 

6'  8"  X  6'  8" 

9M 

6 

0.85 

27-He" 

19_7^6* 

3.85 

21X21 

4'  9" 

7'  0"  X  7'  0" 

10 

6/4 

0.89 

20  -He" 

21-Ke" 

4.09 

22X22 

5'  0" 

7'  4"  X  7'  4" 

6*4 

0.94 

33-Ke" 

4.20 

23X23 

5'  3" 

7'  8"  X  7'  8" 

1  1 

7 

0.99 

35   He" 

23-He" 

25—  He" 

4.40 

24X24 

5'  6" 

8'  0"X8'  0" 

11% 

7K 

1.05 

39-Ke" 

25-Ke" 

26-He" 

4.55 

25X25 

5'  9" 

8'  4"X8'  4" 

I2H 

73'£ 

1.10 

33-M" 

23-^" 

4.78 

26X26 

6'  0" 

8'8"X8'  8" 

8 

1.15 

35-^" 

25-K" 

26-K" 

5.15 

Superimposed  load  =  350  Ib.  per  sq.  ft. 

• 

Round  steel  rods  in  each  band 

Panel 
size 
(feet) 

Capital 
diam- 
eter 

Size  of 
drop  panel 

Depth 
of  slab 
(inches) 

Depth 
of  drop 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Across 
direct 

Diagonal 

16X16 

3'  6" 

5'4"X5'  4" 

8 

4H 

0.71 

24-%" 

16-%" 

17-%" 

3.20 

17X17 

3'  9" 

5'  8"X5'  8" 

8/^ 

5% 

0.76 

27-%" 

18-%" 

19-%" 

3.36 

18X18 

4'  0" 

6'  0"  X  6'  0" 

9 

5/-^ 

0.80 

23-He" 

16-Ke" 

3.64 

19X19 
20X20 

4'  3" 
4'  6" 

6'  4"  X  6'  4" 
6'  8"  X  6'  8" 

10  2 

6 

0.84 
0.89 

25   He" 
27-H'e" 

17-Ke" 
19-Ke" 

18-Ke" 
20-  1{  6  " 

3.82 
4.00 

21X21 
22X22 
23  X  23 
24X24 

4'  9" 
5'  0" 
5'  3" 
5'  6" 

7'0"X7'0" 
7'  4"X7'  4" 
7'  8"X7'8" 
8'  0"X8'  0" 

12  * 

p 

0.95 
.00 
.07 
.12 

31-Ke" 

Ijirk 

20-Ke" 
22-Ke" 
25-Ke" 

22-He" 
24-He" 

ttfy" 

4.24 
4.42 
4.63 
4.76 

25X25 

5'  9" 

8'  4"X8'  4" 

13 

8 

.16 

34-  \/  " 

23—i^" 

5.00 

26X26 

6'  0* 

8'  8"X8'  8" 

13?i 

.22 

38-M" 

25-H" 

26-M" 

5.29 

44 


TABLE  13 


FLAT  SLAB  FLOORS 
CHICAGO  BUILDING  CODE 
INTERIOR  SQUARE  PANELS 


FLAT 
SLABS 


CAP  CONSTRUCTION 

fc  =  700  for  positive  moment 
fc  =805  for  negative  moment 
fs=18,000 
n=15 


Superimposed  load  =  100  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Add'l  in  each 
band  over 
each  column 

Across 
direct 

Diagonal 

16X16 

3'  6* 

6% 

0.562 

13-% 

o  S/ 

9-% 

9-% 

2.17 

17X17 

3'  9* 

0.604 

14—% 

10—^ 

10-% 

10-% 

2.34 

18X18 

4'0* 

7% 

0.646 

16-% 

H-% 

H-% 

H-% 

2.46 

19X19 

4'  3* 

8 

0.667 

12-% 

13-% 

13-% 

2.69 

20X20 

4'  6" 

8K 

0.708 

21—% 

14-% 

14-% 

14-% 

2.85 

21X21 

4'  9" 

9 

0.750 

17-Ke* 

12-K 

3.04 

22X22 

5'0* 

0.792 

19-Ke" 

13-K 

13_j^6* 

3.23 

23X23 

5'  3*                9% 

0.812 

21-Ke" 

15-K 

14—  K  6* 

14-K 

3.40 

24X24 

5'  6*              10% 

0.854 

24-K6* 

16-K 

16-K  6* 

16-K 

3.65 

25X25 

5'  9*              10% 

0.896 

26-K6" 

17-K 

18  ~K  K" 

18-K 

3.85 

26X26 

6'0*              UX 

0.937 

19-K 

19-He' 

19-K  * 

3.97 

Superimposed  load  =  150  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

.    Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Add'l  in  each 
band  over 

Across        Diagonal 

each  column 

16X16 

3'  6" 

7K 

0.625 

15-% 

10-%* 

10-% 

10-% 

2.50 

17X17 

3'  9" 

8 

0.667 

17-% 

11-%* 

H-% 

11-% 

2.65 

18X18 

4'0* 

0.708 

19-% 

12-%* 

13-% 

13-% 

2.83 

19X19 

4'  3* 

9 

0.750 

21-% 

14-%* 

14-% 

14-% 

2.96 

20X20 

4'  6" 

0.771 

24-% 

16-%* 

17-% 

17-% 

3.32 

21X21 

4'  9" 

10 

0.833 

20-K«" 

13-Ke" 

13—  K 

13—  K 

3.46 

22X22 

0.875 

22-Ke* 

15—  K 

15—  K 

3.67 

23X23 

5'  3" 

11 

0.917 

24-Ke" 

lg_7^  K" 

16-K 

3.83 

24X24 

5'  6* 

0.958 

26-K«* 

17-K«" 

18-K 

18-K 

3.96 

25X25 

5'  9* 

12 

1.000 

29-Ke" 

19—  KB* 

20-K 

20-K  6 

4.26 

26X26     i       6'  0* 

1.042 

16-H" 

4.54 

Superimposed  load  =  200  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Add'l  in  each 
band  over 
each  column 

Across 
direct 

Diagonal 

16X16 

3'  6* 

8^ 

0.687 

16-%* 

n-%" 

H-% 

n-% 

2.76 

17X17 

3'  9" 

8% 

0.729 

18-%* 

13-% 

13-% 

2.95 

18X18 

4'0* 

0.771 

15-K  6 

10—  Ks* 

ll-K 

3.21 

19X19 

4'  3* 

o  &/ 

0.813 

17-K« 

12-K  6* 

12—  K 

12-K 

3.42 

20X20 

4'  6" 

10^4 

0.854 

20-K  6 

13-K 

13-K 

3.60 

21X21 

4'  9" 

10% 

0.896 

22-Kc 

14-K  e" 

15-K 

15-K 

3.82 

22X22 

5'  0" 

11  \^L 

0.937 

24-Ke 

16—  K 

16-K 

4.00 

23X23 

5'  3* 

12 

1.000 

13—  1^" 

14—  14 

4.21 

24X24 

5'  6" 

12M 

1.042 

23->i* 

14—  £•£* 

15~M 

15~M 

4.46 

25X25 

5'  9* 

13                   1.083 

25-M* 

1  Q—1,4  " 

17—  M 

17_i^ 

4.76 

26X26 

6'0*               13H                1-125 

27->i* 

i8-yz" 

i*4j 

18-H 

4.94 

45 


FLAT 
SLABS 


TABLE  IS 


FLAT  SLAB  FLOORS 
CHICAGO  BUILDING  CODE 
INTERIOR  SQUARE  PANELS 


CAP  CONSTRUCTION 

/c  =700  for  positive  moment 
fc  =805  for  negative  moment 
fs=18,000 
n=15 


Superimposed  load  =  250  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

1 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ibs.  per 
sq.  ft. 

Direct 

Add'l  in  each 
band  over 
each  column 

Across 
direct 

Diagonal 

16X16 

3'  6" 

9 

0.750 

17-%" 

n-%" 

12-%" 

12-%" 

2.92 

17X17 

3'  9" 

0.792 

13_s^/> 

13-%" 

13-%" 

3.12 

18X18 
19X19 
20X20 

4'  0" 
4'  3" 
4'  6" 

10 

1  1  \A 

0.833 
0.896 
0.937 

19-Me" 
21-He" 

jjjjjj: 

13-Ke" 

13-Ke" 
14-J-le" 

3.42 
3.67 
3.86 

21X21 

4'  9" 

11% 

0.979 

15—  7.Y«" 

1  6-  7-<"  c  " 

16-Ke" 

4.05 

22X22 

5'  0" 

1.042 

20-3-i" 

13-3-2" 

13-3-2" 

13->2 

4.29 

23X23 

5'  3" 

133-1 

1.104 

21  —  \4t" 

14-jJ* 

15—3-2" 

15_L£ 

4.51 

24X24 

5'  6" 

14 

1.167 

24-3-2  " 

Jg-l^l' 

16-3-2 

4.71 

25X25 

5'  9" 

143-2 

1.208 

26-3-2" 

16—  !,£" 

17—3-2  " 

17—3-2 

4.91 

26X26 

6'  0" 

15^ 

1.271 

28-3-2" 

18-X2" 

19-H" 

19->2 

5.13 

Superimposed  load  =  300  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

A4d'l  in  each 
band  over 
each  column 

Across 
direct 

Diagonal 

I 

16X16 

3'  6" 

103-4 

0.854 

18-%" 

H-%" 

12-%" 

12-^" 

3.01 

17X17 

3'  9" 

11 

0.917 

10-Kc 

3.20 

18X18 

4'  0" 

113-2 

0.958 

17-Me" 

11—  M 

1  1-J.fg 

ii-Ko 

3.42 

19X19 

4'  3" 

1224 

1.021 

19-Ke" 

12-K 

13—  J-Y  « 

3.67 

20X20 

4'  6" 

13 

1.083 

13-H 

14-Ke 

14-Ke 

3.80 

21X21 

4'  9" 

133-2 

1.125 

23—  J-f  e" 

15-H 

4.05 

22X22 

5'  0" 

1434 

1.187 

20—^2" 

13—  3-2 

13—  3-2" 

4.27 

23X23 

5'  3" 

15 

1.250 

22-3V' 

14-3*2 

14-3-2 

14-3-2" 

4.47 

24X24 

5'  6" 

16 

1.333 

24-3-2" 

15—  l-o' 

Ig—i^ 

jg—i,^" 

4.71 

25X25 

5'  9" 

17 

1.417 

16-3-2 

17-3-2 

17-3-2" 

4.84 

26X26 

6'0" 

17% 

1.479 

28-3-2" 

18-J-2 

19-H 

19->2" 

5.13 

Superimposed  load  =  350  Ib.  per  sq.  ft. 

Panel  size 
(feet) 

Capital 
diameter 

Depth 
of  slab 
(inches) 

Concrete 
in  cubic 
feet  per 
sq.  ft. 

Round  steel  rods  in  each  band 

Steel  in 
Ib.  per 
sq.  ft. 

Direct 

Add'l  in  each 
band  over 
each  column 

Across 
direct 

Diagonal 

16X16            3'  6" 
17X17            3'  9" 
18X18            4'  0" 
19X19            4'  3" 

!$ 

13 

0.958 
1.021 
1.083 
1.146 

18-%" 
15-Ke" 
17-Ke" 
19-Ke" 

io-K«* 

12-He" 

11~?i«C 

H-Ke" 
13-He" 

3.01 
3.28 
3.42 
3.67 

20X20            4'  6" 

14>2 

1.208 

14—  J-f  e" 

14-Me" 

3.86 

21X21             4'  9" 

15J4 

1.271 

23—  J--f  «" 

15—  M  e" 

16—  M  e" 

4.05 

22X22 

5'  0" 

163^ 

1.354 

20—  V2  " 

13—3^" 

13—3-2" 

13—3-2" 

4.29 

23X23 

5'  3" 

17K 

1.437 

22-^" 

14-3-2" 

14-3-2" 

14-3-2" 

4.47 

24X24 

5'  6" 

1.521 

23-3-2" 

15-3-2" 

lg_  i^" 

jg_i^^ 

4.64 

25X25 

5'  9" 

19 

1.583 

17-3-2" 

17_i<£" 

17—3-2  " 

4.91 

26X26 

6'  0* 

20 

1.667 

28-M" 

19-3-2" 

19-M" 

5.13 

46 


SECTION  3 
RECTANGULAR  BEAMS 

Table  14  and  Diagram  18  may  be  used  in  the  design  of  rectangular  beams.  Dia- 
gram 18  may  also  be  employed  to  determine  the  safe  resisting  moment  of  a  given  beam 
and  the  greatest  unit  stresses  due  to  a  given  bending  moment. 

Example  of  Design  of  Rectangular  Beam 

Design  a  simply  supported  rectangular  beam  to  carry  a  total  load,  of  3000  Ib.  per  ft.  on 
a  span  of  20ft.;fe  =  650;  /.  =  16,000;  n  =  15. 

Reading  from  the  intersection  of  lines  representing  fc  =  650  and  /,  =  16,000  in 

Diagram  18,  it  is  found  that  ^  =  107.5  and  j  =  0.875  (Table  14  gives  values  of 
107.7  and  0.874  respectively). 

a  -  f  =  (300°s)(20);(12)  -  1,800,000  in.*. 

o  o 


-  16'75° 


Assuming  b  =  14  in.     d  =  34.5  in. 

M  '  _  1,800,000  o7« 

"A/a  "  (16,000)  (0.875)  (34.5)  " 

or  As  =  (0.0077)  (14)  (34.5)  =  3.72  sq.  in. 

From  Table  15  which  gives  areas  and  perimeters  of  combinations  of  four  rods,  we 
find  that  the  area  of  three  1^-in.  and  one  1-in.  round  rods  is  3.77  sq.  in. 

To  make  a  complete  design,  the  bond  stress  and  shearing  stress  should  also  be 
investigated. 

Reviewing  Design  of  Rectangular  Beam 

Given  a  beam  12  in.  wide,  30  in.  deep  to  steel,  reinforced  with  four  l-in.  round  rods 
and  subjected  to  a  bending  moment  of  1,500,000  in.-lb.  Find  the  unit  stresses  in  the 
steel  and  concrete,  n  =  15. 

M_        1,500,000  _ 

bd*        (12)  (30)2 

'-  KF  -  -  °-°°87 


From  Diagram  18 

fe  =  805  and  /.  =  18,200 

Using  Diagrams  for  Rectangular  Beams  One  Inch  Wide 

Design  a  rectangular  beam  to  resist  a  moment  of  1,000,000  in.-lb.,  assuming  fc  =  750 
andf,  =  18,000. 

Taking  b  =  12  in.,  the  bending  moment  per  inch  of  width  is 

^0°0  =  83,333  in,lb. 

Then  from  Diagram  24 

d  =  26  in.  and  A,  =  (12)  (0.204)  =  2.448  sq.  UL, 
47 


RECTANGULAR  BEAMS 

Finding  Points  to  Bend  Horizontal  Steel 

Diagram  25  is  for  use  in  determining  the  points  at  which  horizontal  steel  in  beams 
or  slabs  can  be  bent  so  that  the  steel  remaining  will  not  be  less  than  that  required  to 
take  the  bending  moment.  The  curves  in  the  lower  left  hand  corner  are  maximum 
bending  moment  curves  for  the  center  and  supports  of  beams  for  different  conditions  of 
loading  and  restraint.  They  give  the  proportion  of  the  steel  required  at  different 
points  along  the  beam  from  support  to  center. 

How  far  from  the  support  of  a  simple  beam  of  2Q-ft.  span,  uniformly  loaded,  can  four 
tenths  (0.4)  of  the  steel  be  bent  up? 

Using  the  scale  which  reads  up  from  the  bottom,  enter  at  0.4  and  follow  hori- 
zontally to  the  curve  marked  "uniform  load,  simple  span,  bottom  steel."  The  bend 
point  is  shown  to  be  0.183  of  the  span  length  from  the  support.  Following  up  to  the 
line  for  a  20-ft.  span  and  then  horizontally  to  the  right  hand  scale,  this  distance  is 
found  to  be  44  in.  from  the  support. 


48 


TABLE  14 


RECTANGULAR 
BEAMS 


VALUES  OF  Ar,  /,  p  AND  K 


nfc 


K  = 


n  =  12 

/• 

fc 

k 

3 

P 

K 

/. 

fc 

k 

3 

P 

K 

500 

0.300 

0.900 

0.0054 

67.5 

. 

500 

0.261 

0.913 

0.0038 

59.6 

550 

0.320 

0.893 

0.0063 

78.7 

550 

0.280 

0.907 

0.0045 

69.4 

600        0.340 

0.887 

0.0073 

90.5 

600 

0.298 

0.901 

0.0053 

80.5 

650        0.358 

0.881 

0.0083 

102.5 

650 

0.315 

0.895 

0.0060 

91.6 

14,000 

17,000 

700        0.375 

0.875 

0.0094 

114.8 

700 

0.331 

0.890 

0.0068 

103.1 

750        0.391 

0.870 

0.0105 

127.6 

750 

0.346 

0.885 

0.0076 

114.7 

800 

0.407 

0.864 

0.0116 

140.6 

800 

0.361 

0.880 

0.0085 

127.1 

850 

0.421 

0.860 

0.0128 

154.0 

850 

0.375 

0.875 

0.0094 

139.5 

900 

0.435 

0.855 

0.0140 

167.4 

900 

0.389 

0.870 

0.0103 

152.2 

500 

0.286 

0.905 

0.0048 

64.7 

500 

0.250 

0.917 

0.0035 

57.2 

550 

0.306 

0.898 

0.0056 

75.5 

550 

0.268 

0.911 

0.0041 

67.2 

600 

0.324 

0.892 

0.0065 

86.7 

600 

0.286 

0.905 

0.0048 

77.6 

650 

0.342 

0.887 

0.0074 

98.6 

650 

'  0.302 

0.899 

0.0055 

88.4 

15,000 

18,000 

700 

0.359 

0.880 

0.0084 

110.4 

700 

0.318 

0.894 

0.0062 

99.6 

750 

0.375 

0.875 

0.0094 

123.4 

750 

0.333 

0.889 

0.0069 

111.1 

800 

0.390 

0.870 

0.0104 

135.7 

800 

0.348 

0.884 

0.0077 

123.0 

850        0.405 

0.865 

0.0115 

149.2 

850 

0.362 

0.879 

0.0085 

135.2 

I  900        0.418 

0.861 

0.0125 

162.0 

900 

0.375 

0.875 

0.0094 

147.7 

500 

0.273 

0.909 

0.0043 

62.0 

500 

0.231 

0.923 

0.0029 

53.3 

550 

0.292 

0.903 

0  .  0050 

72.5 

550 

0.248 

0.917 

0.0034 

62.6 

600 

0.310 

0.897 

0.0058 

83.5 

600 

0.265 

0.912 

0.0040 

72.6 

650 

0.328 

0.891 

0.0067 

94.9 

650 

0.281 

0.906 

0.0046 

82.7 

16,000 

20,000 

700 

0.344 

0.885 

0.0075 

106.7 

700 

0.296 

0.901 

0.0052 

93.3 

750 

0.360 

0.880 

0.0084 

118.8 

750 

0.310 

0.897 

0.0058 

104.3 

800 

0.375 

0.875. 

0.0094 

131.3 

800 

0.324 

0.892 

0.0065 

115.6 

850 

0.389 

0.870 

0.0103 

144.0 

850 

0.338 

0.887 

0.0072 

127.4 

900 

0.403 

0.866 

0.0113 

157.0 

900 

0.351 

0.883 

0.0079 

139.4 

n  =  15 

/.                 fc 

k 

i 

P 

K                f. 

fc 

k 

3 

P 

K 

500 

0.349 

0.884 

0.0062 

77.1 

500 

0.306 

0.898 

0.0045 

68.7 

550 

0.371 

0.876 

0.0073 

89.4 

550 

0.327 

0.891 

0.0053 

80.1 

600 

0.391 

0.870 

0.0084 

102.1 

600 

0.346 

0.885 

0.0061 

91.8 

650 

0.411 

0.863 

0.0095 

115.2 

650 

0.365 

0.878 

0.0070 

104.2 

14,000 

17,000 

700 

0.429 

0.857 

0.0107 

128.6 

700 

0.382 

0.873 

0.0079 

116.7 

750 

0.446 

0.851 

0.0120 

142.2 

750 

0.398 

0.866 

0.0088 

129.2 

800 

0.462 

0.846 

0.0132 

156.3 

800 

0.414 

0.862 

0.0097 

142.7 

850 

0.477 

"  0.841 

0.0145 

170.4 

850 

0.429 

0.857 

0.0107 

155.9 

900 

0.491 

0.836 

0.0158 

184.8 

900 

0.443 

0.853 

0.0117 

169.7 

500 

0.333 

0.889 

0.0056 

74.1 

500 

0.294 

0.902 

0.0041 

66.3 

550 

0.355 

0.882 

0.0065 

86.4 

550 

0.314 

0.895 

0.0048 

77.4 

600 

0.375- 

0.875 

0.0075 

98.4 

600 

0.333 

0.889 

0.0056 

88.9 

650 

0.394 

0.869 

0.0085 

111.3 

650 

0.351 

0.883 

0.0063 

100.8 

15,000 

18,000 

700 

0.412 

0.863 

0.0096 

124.4 

700 

0.368 

0.877 

0.0072 

113.1 

750 

0.428 

0.857 

0.0107 

137.6 

750 

0.385 

0.872 

0.0080 

125.7 

800 

0.444 

0.852 

-   0.0118 

151.2 

800 

0.400 

0.867 

0.0089 

138.7 

850 

0.460 

0.847 

0.0130 

165.1 

850 

0.415 

0.862 

0.0098 

151.9 

900 

0.474 

0.842 

0.0142 

179.5 

900 

0.429 

0.857 

0.0107 

165.3 

500 

0.319 

0.894 

0.0050 

71.3 

500 

0.273 

0.909 

0.0034 

62.0 

550 

0.339 

0.887 

0.0058 

82.9 

550 

0.292 

0.903 

0.0040 

72.5 

600' 

0.360 

0.880 

0.0068 

95.0 

600 

0.310 

0  .  897 

0.0047 

83.5 

650 

0.379 

0.874 

0.0077 

107.7 

650 

0.328 

0.891 

0.0053 

94.9 

16,000 

20,000 

700 

0.396 

0.868 

0.0087 

120.4 

700 

0.344 

0.885 

0.0060 

106.6 

750 

0.413 

0.862 

0.0097 

133.5 

750 

0.360 

0.880 

0.0068 

118.8 

800 

0.429 

,0.857 

0.0107 

146.9 

800 

0.375 

0.875 

0.0075 

131.2 

850 

0.443 

0.852 

0.0118 

160.6  i' 

850 

0.389 

0.870 

0.0083 

144.0 

• 

900 

0.458 

0.847 

0.0129 

174.5 

900 

0.403 

0.866 

0.0091 

157.0 

49 


RECTANGULAR 
BEAMS 


DIAGRAM   18 


VALUES  OF  k,  j,  p  AND  K 
71=75 


rercentaqe  of  steel 


DIAGRAM  19 


\ 

RECTANGULAR 
BEAMS 

MOMENT  OF  RESISTANCE  AND  AREA  OF  STEEL 

FOR 
BEAMS  ONE  INCH  WIDE 


fe=650 
fs=16,0 
=  15 


Area  or  steel  in  so.  in. 


RECTANGULAR 
BEAMS 


DIAGRAM  20 


fc=650 
fs=18,0 
n=15 


MOMENT  OF  RESISTANCE  AND  AREA  OF  STEEL 

FOR 
BEAMS  ONE  INCH  WIDE 


DIAGRAM  21 


RECTANGULAR 
BEAMS 


MOMENT  OF  RESISTANCE  AND  AREA  OF  STEEL 

FOR 
BEAMS  ONE  INCH  WIDE 


fe=700 
f,=16, 


Area  of  stee    in  sg.  in. 


RECTANGULAR 
BEAMS 


DIAGRAM  22 


fc=700 
fs=18,0 
n=15 


MOMENT  OF  RESISTANCE  AND  AREA  OF  STEEL 

FOR 
BEAMS  ONE  INCH  WIDE 


Area  or  steel    m  sa.  in 


RECTANGULAR 
BEAMS 


MOMENT  OF  RESISTANCE  AND  AREA  OF  STEEL 

FOR 
BEAMS  ONE  INCH  WIDE 


fe  =  750 
f,  =  16,000 


Area    or  steel  in  sq.  in. 


RECTANGULAR 
BEAMS 


DIAGRAM  24 


/  =750  MOMENT  OF  RESISTANCE  AND  AREA  OF  STEEL 

ft  =18,000  FOR 

n=15  BEAMS  ONE  INCH  WIDE 


Area    of  stee    m  sa.  in. 


DIAGRAM  25 


RECTANGULAR 
BEAMS 


DIAGRAM  FOR  LOCATING  POINTS 
TO  BEND  HORIZONTAL  STEEL 


RECTANGULAR 
BEAMS 


AREAS  AND  PERIMETERS 

OF 
COMBINATIONS  OF  FOUR  RODS 


Square  rods 

Number  and  size                                                 Round  rods 

II 

Area 

(sq.  in.) 

Perimeter 
(in.) 

M 

H 

H 

y* 

1 

1H       IK 

Area 

(sq.  in.) 

Perimeter 

(in.) 

1  00 

80                  4 

1 

0  79 

6  28 

l!l4 

8  .  5                  3 

l 

0.89 

6^68 

1.28 

9.0                  2 

2 

1.01 

7.07 

1  31 

90             i      3 

1 

1   03 

7  07 

l'42 

9.5                   1 

3 

1.12 

7^46 

1.52 

9.5 

3 

i 

1.19 

7.46 

1.56 

10.0 

4 

1.23 

7.85 

1.63 

10.0 

2' 

2 

1.28 

7  85 

1.73 

10.5 

3 

1 

1.36 

8.25 

1.91 

11.0 

2 

2 

1.50 

8.64 

1.94 

11.0 

3 

i 

1.52 

8.64 

1.94 

11.0 

l" 

3 

1.52 

8   64 

2.03 

11.0 

2 

2 

;;  \  '.'. 

1.60 

8.64 

2.08 

11.5 

i 

3 

1.63 

9.03 

2.17 

11.5 

3 

i 

1.71 

9.03 

2.25 

12.0 

4 

1.77 

9.43 

2.31 

'      12.0 

2 

2 

1.82 

9.43 

2.45 

12.5 

3 

1 

1.93 

9.82 

2.55 

12.5 

'l 

3 

2.00 

9   82 

2.66 

13.0 

2 

2 

2.09 

10.21 

2.69 

13.0 

1 

3  

2.11 

10.21 

2.69 

13.0 

3 

i       .... 

2.11 

10.21 

2.78 

13.0 

2 

2        !       .-        ;       •- 

2.18 

10  21 

2.86 

13.5 

1 

3 

2.24 

10.60 

2.95 

13.5 

3 

"         " 

1 

2.32 

10  .  60 

3.06 

14.0 

- 

4 

2.41 

11.00 

3.13 

14.0 

2 

2           .  . 

2.45 

11  .00 

3.30 

14.5 

3           1           .  . 

2.59 

11   39 

3.39 

14.5 

"l 

3 

2.66 

11.39 

3.53 

15.0 

2           2 

2.77 

11.78 

3.56 

15.0 

1 

3 

2.80 

11.78 

3.56 

15.0 

3          ..           1 

2.80 

11.78 

3.66 

15.0 

2 

.  .     i     .  .     i      2 

2.87 

11.78 

3.77 

15.5 

1          3     I     .. 

2.96 

12.  17 

3.86 

15.5 

.  .          .  . 

3          .... 

'l 

3.03 

12.17 

4.00 

16.0 

_ 

..     1     .. 

4 

3.14 

12.56 

4.06 

16.0 

I 

2       .  ;       2 

3.19 

12,56 

4.27 

16.5 

_ 

31 

3.35 

12.96 

4.36 

16.5 

1 

.  .     |     .  .          3 

3.42 

12.96 

4.53 

17.0 

2           2 

3.56 

13.35 

4.56 

17.0 

3     ; 

1 

3.58 

13.35 

4.56 

17.0 

i 

3 

3.58 

13.35 

4.66 

17.0 

2 

2 

3.66 

13.35 

4.80 

17.5 

V 

3 

3.77 

13.74 

5.06 

18.0 

4 

3.98 

14.14 

5.13 

18.0 

2 

2 

4.02 

14.14 

5.36 

18.5 

3 

1 

4.21 

14.53 

5.45 

18.5 

1 

3 

4.28                        14.53 

5.66 

19.0 

2 

2 

4.44 

14.92 

5.69 

19.0 

1 

3 

4.47 

14.92 

5.95 

19.5 

1 

3 

4.67 

15.32 

6.25 

20.0 

4 

4.91 

15.71 

58 


TABLE  16 


RECTANGULAR 
BEAMS 


AREAS  AND  PERIMETERS 

OF 
COMBINATIONS  OF  SIX  RODS 


1 

| 

Square  rods 

Number  and  size 

Round  rods 

Square  rods 

Number  and  size 

Round  rods 

Area 

Perim- 

Area 

Perim- 

Area 

Perim- 

Area 

Perim- 

(sq.    1     eter 

N 

^ 

% 

1 

IK 

IK 

(sq. 

eter 

(sq. 

eter 

N 

;!i 

H 

1 

IK 

IK 

(sq. 

eter 

in.) 

(in.) 

in.) 

(in.) 

in.) 

(in.) 

in.) 

(in.) 

2.34 

15.0 

ft 

1.84 

11.78 

5.39 

22.5 

*  " 

5 

1 

4.23 

17.67 

2.52 

15.5 

5 

I 

\'m 

\\ 

1.98 

12.17 

5.48 

22.5 

3 

3 

4.31 

17.67 

2.69 

16.0 

4 

9 

2.11 

12.57 

5.53 

23.0 

2 

4 

4.34 

18.07 

2.72 

16.0 

5.. 

1 

2.14 

12.57 

5.56 

23.0 

1 

5 

4.37 

18.07 

2.86 

16.5 

3 

3 

2.25 

12.96 

5.59 

23.0 

4 

2 

4.39 

18.07 

2.95 

16.5 

5 

1 

2.32 

12.96 

5.77 

23.5 

1 

5 

4.53 

18.46 

3.03 

17.0 

2 

4 

2.38 

13.35 

6.00 

24.0 

6 

4.71 

18.85 

3.09 

17.0 

4 

.  t 

2 

2.43 

13.35 

6.09 

24.0 

3 

3 

4.79 

18.85 

3.20 

17.5 

1 

5 

2.52 

13.74 

6.19 

24.0 

2 

4 

4.86 

18.85 

3.38 

18.0 

6 

•• 

2.65 

14.14 

6.19 

24.0 

4 

2 

4.86 

18.85 

3.47 

18.0 

3 

3 

2.72 

14.14 

6.27 

24.5 

.. 

.. 

.. 

5 

1 

4.92 

19.24 

3.56 

18.0 

4 

2 

2.80 

14.14 

6.53 

25.0 

4 

2 

5.13 

19.64 

3.58 

18.5 

5 

1 

'] 

2.81 

14.53 

6.56 

25.0 

5 

1 

5.15 

19.64 

3.78 

19.0 

4 

2 

2.97 

14.92 

6.59 

25.0 

2 

4 

5.18 

19  64 

3.81 

19.0 

6 

1 

2.99 

14.92 

6.80 

25.5 

•• 

3 

3 

5.34 

20.03 

3.84 

19.0 

2 

4 

.. 

3.02 

14.92 

6.89 

25.5 

•  1 

5 

. 

.5.41 

20.03 

3.98 

19.5 

. 

3 

3 

. 

3.13 

15.32 

6.98 

25.5 

3 

. 

3 

5.48 

20.03 

4.08 

19.5 

5 

1 

.  . 

3.20 

15.32 

7.06 

26.0 

2 

4 

5.55 

20.42 

4.17 

19.5 

3 

3 

3.28 

15.32 

7.09 

26.0 

1 

5 

5.57 

20.42 

4.19 

20.0 

2 

4 

3.29 

15.71 

7.13 

26.0 

-• 

4 

2 

5.60 

20.42 

4.22 

20.0 

1 

5 

3.31 

15.71 

7.33 

•    26.5 

1 

5 

5.76 

20.81 

4.25 

20.0 

4 

2 

3.34 

15.71 

7.59 

27.0 

6 

5.96 

21.20 

4.39 

20.5 

. 

1 

5 

3.45 

16.10 

7.69 

27.0 

3 

3 

6.04 

21.20 

4.59 

21.0 

6 

3.61 

16.49 

7.78 

27.0 

2 

4 

6.11 

21.20 

4.69 

21.0 

3 

3 

•• 

3.68 

16.49 

7.89 

27.5 

•• 

•• 

5 

1 

6.19 

21.60 

4.78 

21.0 

2 

4 

3.76 

16.49 

8.19 

28.0 

4 

2 

6.43 

21.99 

4.78 

21.0 

4 

2 

3.76 

16.49 

8.25 

28.0 

2 

4 

6.48 

21.99 

4.83 

21.5 

5 

1 

;  . 

3.79 

16.89 

8.48 

28.5 

3 

3 

6.66 

22.38 

5.06 

22.0 

.  . 

4 

2 

3.98 

17.28 

8.58 

28.5 

1 

5 

6.74 

22.38 

5.09 

22.0 

5 

1 

4.00 

17.28 

8.78 

29.0 

2 

4 

6.90 

22.78 

5.13 

22.0 

3 

4 

4.03 

17.28 

8.81 

29.0 

1 

5 

6.92 

22.78 

5.30 

22.5 

3 

3 

!  4.16 

17.67 

9.08 

29.5 

1 

5 

7.13 

23.17 

5.39 

22.5 

1 

5 

4.23 

17.fi7 

9.38 

30.0 

6 

7.36 

23.56 

59 


RECTANGULAR 
BEAMS 


TABLE  17 


AREAS  AND  PERIMETERS 

OF 
COMBINATIONS  OF  EIGHT  RODS 


Square  rods 

Number  and  size 

Round  rods          Square  rods 

Number  and  size 

I 
;     Round  rods 

Area 

Perim- 

Area 

Perim-     Area 

Perim- 

Area 

Perim- 

(sq. 

eter 

H 

7A 

1 

IK 

iH 

(sq- 

eter          (sq. 

eter 

3A 

y* 

1 

1M 

1J-4 

(sq. 

eter 

in.) 

(in.) 

in.) 

(in.)         in.) 

(in.) 

in.) 

(in.) 

4.50 

24.0 

8 

3.53 

18.85      8.12 

32.0 

4 

4 

6.38 

25.14 

4.70 

24.5 

7 

l 

3.69 

19.24      8.27 

32.5 

7 

1 

6.49 

25.53 

4.91 

25.0 

6 

2 

3.85 

19.64      8.52 

32.5 

5 

3 

6.69 

25.53 

4.94 

25.0 

7 

1 

3.88 

19.64      8.53 

33.0 

6 

2 

6.70 

25.92 

5.11 

25.5 

5 

3 

4.01 

20.03      8.56 

33.0 

7 

1 

6.72 

25.92 

5.20 

25.5 

7 

1 

4.09 

20.03      8.62 

33.0 

3 

5 

.. 

6.77 

25.92 

5.31 

26.0 

4 

4 

4.17 

20.40      8.72 

33.0 

2 

6 

6.85 

25.92 

5.38 

26.0 

6 

2 

4.22 

20.40     8.80 

33.5 

5 

3 

6.91 

26.31 

5.52 

26.5 

3 

5 

4.33 

20.81      9.06 

34.0 

4 

4 

7.12 

26.70 

5.72 

27.0 

2 

6 

4.49 

21.20      9-12 

34.0 

2 

6 

7.17 

26.70 

5.81 

27.0 

5 

3 

4.57 

21.20      9.13 

34.0 

6 

2 

7.17 

26.70 

5.91 

27.0 

6 

2 

4.64 

21.20      9.31 

34.0 

4 

4 

7.31 

26.70 

5.92 

27.5 

1 

7 

. 

4.65 

21.60      9.33 

34.5 

3 

5 

7.33 

27.10 

6.  12 

28.0 

8 

. 

4.81 

21.99      9.42 

34.5 

1 

7 

7.40 

27.10 

6.25 

28.0 

4 

4 

4.91 

21.99      9.59 

35.0 

2 

6 

7.53 

27.49 

6.36 

28.5 

7 

1 

4.99 

22.38      9.62 

35.0 

1 

7 

7.56 

27.49 

6.59 

29.0 

6 

2 

5.  18 

22.78      9.69 

35.0 

5 

3 

7.61 

27.49 

6.61 

28.5 

5 

3 

5.  19 

22.38      9.86 

35.5 

1 

7 

7.74 

27.88 

6.62 

29.0 

7 

1 

5.20 

22.78    10.11 

35.5 

3 

5 

7.94 

27.88 

6.69 

29.0 

3 

5 

5.25 

22.78    10.12 

36.0 

•• 

8 

7.95 

28.28 

6.83 

29.5 

5 

3 

5.36 

23.17    10.25 

36.0 

4 

4 

8.05 

28.28 

6  92 

29.5 

7 

1 

5.44 

23.17    10.42 

36.5 

7 

1 

8.19 

28.67 

7.06 

30.0 

4 

4 

5.55 

23.56    10.72 

37.0 

,  , 

6 

2 

8.42 

29.06 

7.12 

30.0 

6 

2 

5.60 

23.56    10.81 

37.0 

3 

5 

8.49 

29.06 

7.13 

30.0 

2 

6 

5.60 

23.56    10.91 

37.0 

2 

6 

8.56 

29.06 

7.30 

30.5 

3 

5 

.. 

5.73 

23.96    11.02 

37.5 

.. 

5 

3 

8.65 

29.45 

7.31 

30.0 

4 

4 

5.74 

23.56    11.31 

38.0 

.  . 

4 

4 

8.88 

29.85 

7.53 

31.0 

2 

6 

5.91 

24.35    11.38 

38.0 

. 

2 

6 

8.93 

29.85 

7.56 

31.0 

1 

7 

5.94 

24.35    11.61 

38.5 

3 

5 

9.12 

30.24 

7.63 

31.0 

5 

3 

5.9£ 

24.35    11.70 

38.5 

1 

7 

9.19 

30.24 

7.72 

31.0 

6 

2 

6.06 

24.35    11.91 

39.0 

2 

6 

9.35 

30.63 

7.77 

31.5 

1 

7 

6.10 

24.  74  111  1.94 

39.0 

1 

7 

9.37 

30.63 

8.00 

32.0 

8 

6.28 

25.  14    12.20 

39.5 

1 

7  I 

9.58 

31.02 

8.02 

31.5 

3 

5 

6.30 

24.74    12.50 
1 

40.0 

8   '    9.82' 

31.42 

60 


TABLE  18 


RECTANGULAR 
BEAMS 


AREAS  AND  PERIMETERS 

OF 
GROUPS  OF  RODS  OF  UNIFORM  SIZE 


Number 

Size  of  rods 

H 

H 

M 

M 

H 

H 

1 

1M 

IK 

1H 

1H 

1 
1 

1 
1 

1 

0  .  0625 
1.0 

0.1406 

0.2500 

0.3906 

0.5625 

0.7656 
3.5 

1.000 
4.0 

1.266 

1.563 

1.891 

2.250 

2 

0  .  1250 
2.0 

0.2812 
3.0 

0.5000 
4.0 

0.7812 
5.0 

1.125 
6.0 

1.531 
7.0 

2.000 
8.0 

2.531 
9.0 

3.125 
10  0 

3.781 
11.0 

4.500 
12.0 

3 

0.1875 
3.0 

0.4218 
4.5 

0.7500 
6.0 

1.172 
7.5 

1.688 
9.0 

2.297 
10.5 

3.000 
12.0 

3.797 
13.5 

4.688 
15.0 

5.672 
16.5 

6.750 
18  0 

4 

0.2500 
4.0 

0  .  5624 
6.0 

1.000 
8.0 

1.563 
10.0 

2.250 
12.0 

3.062 
14.0 

4.000 
16.0 

5.062 
18.0 

6.250 
20.0 

7.562 
22.0 

9.000 
24.0 

5 

0.3125 
5.0 

0.7030 
7.5 

1.250 
10.0 

1.953 
12.5 

2.813 
15.0 

3.828 
17.5 

5.000 
20.0 

6.328 
22.5 

7.813 
25.0 

9.453 
27.5 

11.25 
30  0 

6 

0  .  3750 
60 

0.8436 
9.0 

1.500 
12.0 

2.344 
16.0 

3.375 
18.0 

4.594 
21.0 

6.000 
24.0 

7.594 
27.0 

9.375 
30.0 

11.34 
33.0 

13.50 
36.0 

7 

0.4375 
7.0 

0.9842 
10.5 

1.750 
14.0 

2.734 
17.5 

3.938 
21.0 

5.359 
24.5 

7.000 
28  0 

8.859 
31.5 

10.94 
35.0 

13.23 
38.5 

15.75 
42.0 

8 

0.5000 
80 

1.125 
12.0 

2.000 
16.0 

3.125 
20.0 

4.500 
24.0 

6.125 
28.0 

8.000 
32.0 

10.12 
36.0 

12.50 
40.0 

15.12 
44.0 

18.00 
48  0 

9 

0  .  5625 
90 

» 

1.265 
13    5 

2.250 
18.0 

3.516 
22.5 

5.063 
27.0 

6.890 
31.5 

9.000 
36.0 

11.39 
40.5 

14.06 
45.0 

17.02 
49.5 

20.25 
54.0 

10 

0.6250 
10.0 

1.406 
15.0 

2.500 
20  0 

3.906 
25.0 

5.625 
30  0 

7.656 
35.0 

10.00 
40.0 

12.66 
45  0 

15.63       118.91 
50.0           55.0 

22.50 
60.0 

1 

0.0491 
0.785 

0.1105 
1   18 

0.1964 
1.571 

0.3068 
1   96 

0.4418 
2   35 

0.6013 
2   75 

0.7854 
3.14 

0  9940 
3   53 

1.227         1.485 
3  93           4  32 

1.767 
4.71 

2 

0.0982 
1.57 

0  .  2209 
2   36 

0.392*7 
3.14 

0.6136 
3   93 

0.8836 
4  71 

1.203 
5.50 

1.571 
6.28 

1.988 
7.07 

2.454 
7  85 

2.970 
8   64 

3.534 
9.42 

3 

0.1473 
2.36 

0.3313 
3   53 

0.5890 
4.71 

0  .  9204 
5  89 

1.325 
7.07 

1.804 
8  25 

2.356 
9  43 

2.982 
10.6 

3.681 
11.8 

4.455 
13.0 

5.301 
14.1 

4 

0   1964 
3.14 

0.4418 
4.71 

0  .  7854 
6.28 

1.227 
7.85 

1.767 
9   42 

2.405 
11.0 

3.142 
12.6 

3.976 
14.1 

4.908 
15.7 

5.940 
17.3 

7.068 
18.8 

5 

0  .  2455 
3.93 

0  .  5522 
5.89 

0.9817 
7.85 

1.534 
9   82 

2.209 
11.8 

3.006 
13.7 

3.927 
15.7 

4.970 
17.7 

6.135 
19.6 

7.425 
21.6 

8.835 
23   6 

6 

0.2946 
4.71 

0.6627 
7.07 

1.178 
9  43 

1.841 
11  8 

2.651 
14.1 

3.608 
16.5 

4.712 
18  9 

5.964 
21.2 

7.362 
23  6 

8.910 
25.9 

10.60 
28.3 

7 

0.3437 
5.50 

0.7731 
8.25 

1.374 
11.0 

2.148 
13.7 

3.093 
16.5 

4.209 
19.2 

5.498 
22.0 

6.958        8.589 
24.7          27.5 

10.39 
30.2 

12.37 
33.0 

8 

0.3928 
6.28 

0.8836 
9   42 

1.571 
12   6 

2.454 
15  7 

3.534 
18.8 

4.810 
22  0 

6.283 
25.1 

7.952     |  9.816 
28.3     !     31.4 

11.88 
34  6 

14.14 
37.7 

9 

0.4419 
7  07 

0.9940 
10.6 

1.767 
14  1 

2.761 
17.7 

3.976 
21.2 

5.412 
24.7 

7.069 
28  3 

8.946 
31.8 

11.04 
35  3 

13.37 
38  9 

15.90 
42  4 

10 

0.4910 
7.85 

1.105 
11.8 

1.964 
15.7 

3.068 
19.6 

4.418     !   6.013 
23  .  6           27  .  5 

7.854     1  9.940 
31.4     !     35.3 

I 

12.27 
39  3 

14.85 
43.2 

17.67 
47.1 

61 


RECTANGULAR 

BEAMS 


TABLE  19 


AREAS,  PERIMETERS  AND  WEIGHTS  OF  RODS 


Round  rods 

Square  rods 

Size  (inches) 

Area 
(square 
inches) 

Perimeter 
(inches) 

Weight 
per  foot 
(pounds) 

Area 
(square 
inches) 

Perimeter 

(inches) 

Weight 
per  foot 
(pounds) 

H 

0.0491 

0.785 

0.167 

0.0625 

1.00 

0.212 

KG 

0.0767 

0.982 

0.261 

0.0977 

1.25 

0.333 

H 

0.1104 

1.178 

0.375 

0.1406 

1.50 

0.478 

KG 

0.1503 

1.374 

0.511 

0.1914 

1.75 

0.651 

y2 

0.1963 

1.571 

0.667 

0.2500 

2.00 

0.850 

MG 

0.2485 

1.767 

0.845 

0.3164 

2.25 

1.076 

% 

0.3068 

1.964 

1.043 

0.3906 

2.50 

1.328 

% 

0.3712 

2.160 

1.262 

0.4727 

2.75 

1  .  608 

H 

0.4418 

2.356 

1.502 

0.5625 

3.00 

1.913 

13Ae 

0.5185 

2.553 

1.763 

0.6602 

3.25 

2.245 

7/8 

0.6013 

2.749 

2.044 

0  .  7656 

3.50 

2.603 

^6 

0.6903 

2.945 

2.347 

0  .  8789 

3.75 

2  .  989 

1 

O.V854 

3.142 

2.670 

1.0000 

4.00 

3.400 

1M 

0.9940 

3.534 

3.379 

1  .  2656 

4.50 

4.303 

\y± 

1.2272 

3.927 

4.173 

1.5625 

5.00 

5.312 

l3/8 

1.4849 

4.320 

5.049 

1  .  8906 

5.50 

6  .  428 

IX 

1.7671 

4.712 

6.008 

2.2500 

6.00 

7.650 

1% 

2.0739 

5.105 

7.051 

2.6406 

6.50 

8.978 

1% 

2.4053 

5.498 

8.178 

3.0625 

7.00 

10.41 

1% 

2.7612 

5.891 

9.388 

3.5156 

7.50 

11.95 

2 

3.1416 

6.283 

10.68 

4.0000 

8.00 

13.60 

2M 

3.9761 

7.069 

13.52 

5.0625 

'  9.00 

17.22 

2H 

4.9087 

7.854 

16.69 

6.2500 

10.00 

21.25 

2% 

5  .  9396 

8.639 

20.20 

7.5625 

11.00 

25.71 

3 

7.0686 

9.425 

24.03 

9.0000 

12.  CO 

30.60 

62 


SECTION  4 
DOUBLY  REINFORCED  BEAMS 

Diagrams  26  to  30  inclusive  are  particularly  useful  in  checking  the  supports  of  con- 
tinuous T-beams  when  the  value  of  -j-  is  approximately  3^i  o-     The  results  are  on  the 

safe  side  when  -r  is  less  than  %Q.  For  different  values  of  j-^  they  give  directly  the 
amounts  of  compressive  and  tensile  steel  required. 

When  the  value  of  -j-  does  not  approximate  Ho?  the  formulas  given  below  may 

be  used.  These  are  based  on  the  fundamental  fact  that  for  any  given  values  of 
fe  and  /,,  k  has  exactly  the  same  value  regardless  of  the  shape  or  type  of  beam.  It 
follows  from  this  that  if  steel  is  added  to  the  section  without  changing  the  extreme 
fiber  stresses,  this  added  tensile  and  compressive  steel  must  form  a  balanced  couple 
whose  stresses  conform  to  the  stresses  already  in  the  section. 

Let    pi  =  steel  ratio  for  the  beam,  without  compressive  steel. 
p-2  =  steel  ratio  for  the  added  tensile  steel. 

Pf  =  Pi  +  P* 

p'  =  steel  ratio  for  compressive  steel. 
Mi  =  moment  of  the  beam  without  compressive  steel. 
Mz  =  moment  of  the  added  steel  couple. 

M  =  Mi  +  M2 

Then 

I— J- 


Pl  ^  2f* 

^=/*i(i-gw 

3/o  =  M  -  Mi 


P2    = 


1  -  A 

P    •• 


Diagram  31  is  of  general  use.  By  means  of  this  diagram  and  Table  20  it  is  possible 
to  readily  determine  the  stresses  in  the  concrete  and  steel  of  a  doubly  reinforced 
rectangular  beam  for  a  given  bending  moment. 

Diagram  32  is  used  to  determine  the  length  of  embedment  necessary  to  develop  the 
actual  compressive  stress  in  the  rods  in  the  bottom  of  a  continuous  T-beam  at  the 

63 


DOUBLY  REINFORCED  BEAMS 

supports.  The  upper  part  of  the  diagram  is  general,  and  may  be  used  to  find  length 
of  embedment  to  provide  for  bond  when  the  stress  is  the  steel  is  either  tension  or 
compression. 

Finding  Percentages  of  Tensile  and  Compressive  Steel 

M 

~_  What  percentages  of  tensile  and  compressive  steel  will  be  required  when  f  ,.,  =  200, 
t  oa~ 

d' 
iffc  is  not  to  exceed  750  and  /»  is  not  to  exceed  18,000?     j-  =  0.10.     n  =  15. 

From  Diagram  28  we  find  that  for  fc  =  750,  /„  =  18,000,  and  ^  =  200 

p  =  0.0127  and  p'  -  0.010 

If  p  should  be  increased  to  0.0143,  /,  will  be  lowered  to  16,000  and  p'  to  0.0086. 
Given:  b  =  12  in.,  d  =  18  in.,  j  =  0.15,  M  =  750,000  in.-lb.,  fc  =  750  and  /„  = 
16,000,  n  =  15.     Determine  the  required  percentages  of  tensile  aud  compressive  steel. 

From  Table  14, 

k  =  0.413     pi  =  0.0097,  and  K  =  133.5 
M[  =  (133.5)  (12)  (18)2  =  519,000  in.-lb. 
M2  =  750,000  -  519,000  =  231,000  in.-lb. 
231,000 


*       (16,000)  (0.85)  (12)  (18)2 
P  =  Pi  +  p2  =  0.0141 


'  =  (0.0044)  _     =  0.0097 


Finding  Length  of  Embedment  of  Compressive  Steel 

Given  a  continuous  beam  reinforced  with  1-in.  rods  (either  square  or  round)  in  com- 
pression so  that  fc  =  750;  /«  =  16,000;  -7-  =  0.10;  n  =  15;  u  =  80.  Find  required 

length  of  embedment  of  compressive  steel. 

From  the  lower  part  of  Diagram  32,  the  compressive  stress//  is  found  to  be  8540  Ib. 
per  sq.  in.  The  upper  diagram  shows  the  length  of  embedment  for  1-in.  plain  rods, 
with  u  =  80,  to  be  26>2  in. 

Finding  Stresses  in  Concrete  and  Steel 

A  continuous  T-beam,  uniformly  loaded,  has  a  bending  moment  at  the  center  of  each 
span  of  356,300  in.-lb.  Negative  bending  moment  at  the  supports  and  the  positive  bending 

wl2 
moment  at  the  center  of  span  are  figured  by  the  formula,  M  =  ^r.     The  tensile  steel  at  the 

center  of  span  consists  of  four  %-in.  round  bars,     b'  =  10  in.     d   —  15  in.     Design 
the  supports. 

At  the  supports  the  flange  of  the  T-beam,  being  in  tension,  is  negligible  and  the 
T-beam  changes  into  a  rectangular  beam  with  steel  in  top  and  bottom.  Two  of  the 
tension  bars  on  each  side  of  the  supports  will  be  bent  up  and  made  to  lap  over  the  top 
of  the  supports,  while  the  other  two  bars  on  each  side  will  be  continued  straight  and 
lapped  over  supports  at  the  bottom  of  beam. 

64 


DOUBLY  REINFORCED  BEAMS 
The  ratios  of  steel  in  tension  and  compression  are  the  same,  and  are  respectively  : 

a°118 


(1.77  in  above  equation  taken  from  Table  18.) 

d'  -  2  -  o  m 
T     U 

From  Diagram  31,  knowing  p'  =  p,  we  obtain 

d'  k  =  0.361 

For      -  0.10.... 


d'  k  =  0.377 

For       =  0.15... 


Thus, 

k  =0'372 
=  0.873 

(It  is  usually  well  within  the  precision  of  the  actual  work,  and  on  the  safe  side,  to  use  the 
curves  for  the  value  of  -r  next  larger  than  the  actual  value.     Thus  in  this  problem  the 

values  of  k  and  j  for  -j  =0.15  could  be  used  with  sufficient  accuracy.) 

Then 

M  356,300 


(1.77X0.873X15) 
and,  using  Table  20, 

fc  =  n(l  k_  fc)  •/,  =  (0.0394)  (15,400)  =  607  Ib.  per  sq.  in. 

The  stresses  in  the  concrete  and  steel  are  within  the  allowable  and  no  haunch  or 
additional  steel  is  necessary. 

The  moment  of  resistance  at  the  supports  may  be  found  as  follows: 

fen(l  -  k}         650 

fc-      =  0^394  =  16,500  Ib.  per  sq.m. 

Thus  the  moment  of  resistance  depends  on  the  steel  and 

Ms  =  bd%pj  =  (10)  (15)2  (16,000)  (0.0118)  (0.873)  =  371,000  in.-lb. 


65 


DIAGRAM  26 


DOUBLY 
REINFORCED 

BEAMS 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF  ^p,  p,  ANDp' 

*'   JL 

d,     10 


fc=650 
f ,=16,000 
fs  =  18,000 
n=15 


Percentage  of  -tensile  steel,  p 


DOUBLY 
REINFORCED 

BEAMS 


DIAGRAM  27 


ft  =7  00 
f,=16, 
f.=  18,000 
n=15 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF  ~t,  p,  ANDp' 


Percentage  of  tensile  steel, p 


DIAGRAM  28 


DOUBLY 

REINFORCED 

BEAMS 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF  ~,  p,  AN  Dp' 


fe=750 
fs=16,000 
fs=18,000 
=  15 


Percentage  of  tensile  steel ,  p 


DOUBLY 

REINFORCED 

BEAMS 


DIAGRAM  29 


fc=800 

fs=16,000 
fs=  18,000 
15 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF        ,  p,  ANDp' 


Percentage  of  tensi le  steel ,  p 


DIAGRAM  30 


DOUBLY 

REINFORCED 

BEAMS 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF  ^  p,  ANDp' 

<*L=L 
d~  10 


,  fe=850 
f,=16,000 
f,  =  18,000 
71  =  15 


DOUBLY 

REINFORCED 

BEAMS 


DIAGRAM  31 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF  k  AND  j 


DIAGRAM  31 


DOUBLY 
REINFORCED 

BEAMS 


DOUBLY  REINFORCED  RECTANGULAR  BEAMS 
VALUES  OF  k  AND  j 


DOUBLY 

REINFORCED 

BEAMS 


VALUES  OF 


IN  FORMULA  fc 


TABLE  20 


J* 

•48 

<c 

1 
¥ 

-« 

rig 

5' 
1 

¥ 

rH 

- 

2T 
1 

lH 

"s 

^ 

- 

3e 
1 

si 

-4J 

iJS 

5? 

1 

^ 

r4J 

•48 

5 
1 

rH 

"c 

-ie 

* 

-^ 

1 

V 

ri£ 

-Si 

ST 

1 

^ 

| 

I 

0.200 

0.0 

106 

0.2500.0 

222 

0.300 

0.0 

286 

0.350 

0.0 

35!) 

0.400 

0.0 

444 

0.450 

0.0 

545 

0.500 

0.0 

6660.550 

().( 

815 

0.202 

0.0169 

0.2520.0224 

0.302 

0  .  0288 

0.352 

0.0362 

0.402 

0.0447 

0.452 

0.0549 

0.502 

0.0671 

0.5520.0821 

0.204 

0.0171 

0.2540.0226 

0.304 

0.0291 

0.354 

0.0365 

0.404 

0.0451 

0.454 

0.0554 

0.5040.0677 

0  .  554 

0.0827 

0.206 

0.0173 

0.256 

0  .  0229 

0.306 

0.0293 

0.356 

0  .  0368 

0.406 

0.0455 

0.456 

0.0558 

0.506 

0  .  0682 

0  .  556 

0.0834 

0.208 

0.0175 

0.258 

0.0231 

0.308 

0  .  0296 

0.358 

0.0371 

0.408 

0  .  0459 

0.458 

0.0562 

0.508 

0  .  0688 

0.558 

0.0841 

0.210 

0.0177 

0.260 

0.0234 

0.310 

0.0299 

0.360 

0.0375 

0.410 

0.0463 

0.460 

0.0567 

0.510 

0  .  0694 

0.560 

0  .  0848 

0.212 

0.0179 

0.262 

0.0236 

0.312 

0.0301  0.362 

0  .  0378 

0.412 

0  .  0466 

0.462 

0.0571 

0.512 

0.0699 

0.562 

0.0855 

0.214 

0.0181 

0.264 

0.0238 

0.314 

0.0305 

0.364 

0.0381 

0.414 

0  .  0470 

0.464 

0.0576 

0.514 

0.0705 

0.564 

0  .  0862 

0.216 

0.0183 

0.266 

0.0241 

0.316 

0  .  0308 

0.366 

0  .  0384 

0.416 

0.0474 

0.466 

0.0581 

0.516 

0.0711 

0  .  566 

0.0869 

0.218 

0.0186 

0.268 

0.0243 

0.318 

0.0311 

0.368 

0  .  0387 

0.418 

0.0478 

0.468 

0  .  0586 

0.518 

0.0717 

0.568 

0.0876 

0.220 

0.0188 

0.270 

0.0246 

0.320 

0.0314 

0.370 

0.0391 

0.420 

0  .  0482 

0.470 

0.0591 

0.5200.07230.570 

0  .  0884 

0.222 

0.0190 

0.272 

0.0248 

0.322 

0.0317 

0.372 

0.0394 

0.422 

0.0486 

0.472 

0.0595 

0.5220.07280.572 

0.0891 

0.224 

0.0192 

0.274 

0.0251 

0.324 

0.0319 

0.374 

0.0398 

0.424 

0  .  0490 

0.474 

0.0600 

0.5240.0733ji0.574 

0  .  0898 

0.226 

0.0194 

0.276 

0.0254 

0  .  326 

0  .  0322 

0.376 

0.0401 

0.426 

0  .  0494 

0.476 

0.0605 

0  .  526 

0.0739  0.576 

0  .  0905 

0.228 

0.0196 

0.278 

0  .  0257 

0.328 

0.0325 

0.378 

0.0404 

0.428 

0  .  0498 

0.478 

0.0610 

0.5280.07450.578 

0.0912 

0.230 

0.0199 

0.280 

0.0259 

0.330 

0.03280.380 

0  .  0408 

0.430 

0  .  0502 

0.480 

0.0615 

0.5300.0751j|0.580 

0.0920 

0.232 

0.0201 

0.282 

0.0261 

0.332 

0.0331  0.3820.0411 

0  .  432  0  .  0506 

0.482 

0.0620 

0.532  j  0.0757  0.582 

0  .  0927 

0.234 

0  .  0203 

0.284 

0  .  0264 

0.334 

0.0334  0.  384^0.0415 

0.4340.0511 

0.484 

0  .  0625 

0  .  534 

0.0763  0.584 

0.0935 

0.236 

0  .  0205 

0.286 

0.0267 

0.336 

0.03370.3860.0419 

0  .  436 

0.0515 

0.486 

0  .  0630 

0.536 

0.07700.586 

0  .  0943 

0.238 

0  .  0207 

0.288 

0.0269 

0.338 

0.0340 

0.388 

0  .  0422 

0.438 

0  .  0520 

0.488 

0  .  0635 

0.538 

0.07760.588 

0.0951 

0.240 

0.0210 

0.290 

0.0272 

0.340 

0.03440.390 

0.0426 

0.440 

0.0524 

0.490 

0  .  0640 

0.540 

0.0783  0.590 

0.0959 

0.242 

0.0212 

0.292 

0  .  0275 

0.342 

0.03470.392 

0.0429 

0.442 

0  .  0528 

0.4920.0645 

0.542(0.07890.592 

0.0967 

0.244 

0.0214 

0.294 

0.0278 

0.  344  0.0350J  0.394 

0.0433 

0.444 

0  .  0532 

0.4940.0650 

0.544 

0.0795  0.594 

0  .  0975 

0.246 

0.0217 

0.296 

1.0280 

0.346 

0.0353||0.396 

0.0437 

0.446 

0.0536 

0.4960.0656 

0.546 

0  .  0802  0  .  596  0  .  0984 

0.248 

0.0219 

0  .  298 

0  .  0283 

0.348 

0.03560.398 

0.0440 

0.488 

0.0540 

0.4980.0660 

0.548 

0.0808JO.  5980.  0993 

74 


DIAGRAM  32 


DOUBLY 

REINFORCED 

BEAMS 


LENGTH  OF  EMBEDMENT  OF  RODS  IN  COMPRESSION 


UNIT  STRESS  IN  COMPRESSIVE  STEEL 


10 
D 

<5.?o  n  ""s"     ss~"  "*s"  • 

£,  =  \Q  000 

V        X,        "IX.        >s>      o 

"  ^S.           ^"^X.                ^  *    -1                   X-             ^  S^»x_* 

n  *   5 

o.is    .35!      >JjIS    ZS  '   nS^ 

"X.           X^          ^  .        1    y  X^?/") 

"*  s      "^x      ^ix^i-  ^h*? 

1      Xv 

xj     X  ^'Tp^p     ^t 

s.        VN» 

x  /e~    n^O     ^X 

B^^sk 

0.10                                 ^?P     N>            " 

v  v 

x      ^^xT 

^  s^         ^xl          <ss 

ss               X. 

I^V       '          "*  v  ^                  ^v 

X  ^ 

X^             x.         Xs^       ^^ 

sv 

SX_        ^^X               "N.          ^^^ 

o.o5                     ::::::;:: 

S^           ^S                    X^               "*  s                   "  *^ 

020      V        ^  VX       \ 

S                     "XL                ^V               ^\             ^^ 

fs  =  16,000 

>^         »^        T*  ^         x         "*«<  & 

_              _              .                                     .  f~ 

Lii""  s"  '^~  "^;r"&: 

n  =  ID 

o.is         ISIIIS    !.!uj   ^;  ^ 

X,         '  v              ^           rTrPf 

**  I  '         ^v                   SX^ 

S               **  V 

^  >          'S  "^l  '  TrS 

s.             X. 

^^S^^  l^i         ^ 

^X_       ^s 

9.10                                sPM    x 

X             s^          ^                                 i 

^s            ""^  ^ 

^^V                   'V^                    V 

••V                  ^^ 

s              X               X.           sv^ 

ss^ 

**«,.                    *S                     S<i                  >> 

^v                s  ^           X,          ^ss 

005    I 

s  **  i  J__L  ^.      s  >      si     ik 

O                        O                        O                        S? 

\T)                             *O                             r~                              <O 

i     I     II 

Values  of  i'S)  Unit  compress 

ve  stress  in  steel,  Ib.persq.tn. 

75 


SECTION  5 
T-BEAMS 

Diagrams  33  and  34  should  be  used  for  designing  T-beams  when  the  neutral  axis  is 
in  the  stem  and  when  the  compression  in  the  stem  is  to  be  neglected.  The  left  hand 

side  of  the  diagram  gives  the  values  of  r^,  /c,  and  ^-     The  right  hand  side  gives  values 

of  j  and  p,  to  be  used  in  finding  the  area  of  steel  required. 

Diagram  35*  is  for  general  use  and  may  be  employed  either  for  design  or  for 
determining  stresses  in  existing  designs. 

Design  of  T-B  earns 

Assuming  fa  =  16,000,  fc  =  650,  n  =  15,  t  =  5%  in.,  and  M  =  3,000,000  in.-U>., 
find  the  section  of  stem  required. 

Consider  the  stem  width  to  be  12  in.,  and  the  width  of  flange  as  found  from  the 
Joint  Committee  recommendations  to  be  56  in. 

M  t 

To  obtain  the  value  of  r^>  it  is  necessary  to  know  the  value  of  -v     Since  this  is 

unknown  it  must  be  assumed.     For  -,  =  0.2,  Diagram  33  shows  rnr;  =  87.6.  and 

d  oa2 


3^000,000  ,  t         5.5 

=  24-8  m-  and  =     =  °- 


Taking      =  0.23,         =  94,  and 


d  =  J'M^OW       23.9  or  24  in.  and'. 


°-222 


0.229 

a 

The  required  depth  therefore  is  24  in. 

Entering  the  right  hand  side  of  Diagram  33  with  -i  =  0.229  and  K  =  93,  it  is  found 

that  j  =  0.902,  and 

M   -  3,000,000 

"  JITd  ~  (16,000)  (0.902)  (24)  ~ 

Diagram  35  may  also  be  used  in  making  this  design.  The  value  of  -5  is  assumed  as 
before.  Entering  at  the  lower  right  hand  scale  with  /«  =  16,000,  follow  vertically  to 
fe  =  650  and  then  to  the  left  to  ^  =  0.23.  The  percentage  of  steel  is  0.0065.  Now 

follow  vertically  along  -\  =  0.23  to  p  =  0.0065  in  the  upper  left  hand  part  of  the  dia- 
gram.    From  there  follow  to  the  right  to/«  =  16,000  and  then  vertically  to  obtain  the 

value  of  f-T^  =  94. 
oa2 


A. 

*  From  Vol.  I  of  "Bridge  Engineering,"  by  Waddell. 

77 


T-BEAMS 

Usually  the  section  of  the  stem  of  a  T-beam  is  controlled  by  the  shearing  stresses. 
The  procedure  in  ordinary  building  design  is  to  design  the  stem  to  take  the  shear  at  the 
support  and  then  determine  the  concrete  stress  in  the  flange  at  the  center  of  span, 

using  the  value  of  -j  already  determined. 

Reviewing  T-Beams 

M    t 
In  reviewing  a  beam  already  designed,  the  values  of  r-™>  3>  and  p  are  known.     From 

these  the  value  of  fs  is  found  from  the  upper  half  of  Diagram  35.     Then  using  the 
values  of  -v  p  and/s,  the  value  of  fc  is  found  from  the  lower  half  of  this  diagram. 


78 


DIAGRAM  33 


T-BEAMS 


DESIGN  OF  T-BEAMS 
VALUES  OF     L,        fc,  p,  ANDj 


fa=16,000 

71=15 


79 


T-BEAMS 


DIAGRAM  34 


fs=18,000 
n=15 


DESIGN  OF  T-BEAMS 
VALUES  OF  **,     ,  fc,  p,  ANDj 


80 


DIAGRAM  35 


T-BEAMS 


DESIGN  OR  REVIEW  OF  T-BEAMS* 
15 


*  From  Vol.  1  of  "Bridge  Engineering,' 


—  by  Waddell. 
81 


SECTION  6 
SHEAR  REINFORCEMENT 

Diagram  36  may  be  used  to  find  unit  shear  or  bond  stress  for  any  beam. 

Uniformly  Loaded  Beams 

Diagram  37  gives  the  total  number  of  stirrups  in  each  end  of  a  uniformly  loaded 
beam,  assuming  the  concrete  to  take  one-third  of  the  total  shear,  as  recommended  by 
the  Joint  Committee.  The  total  number  -of  stirrups  at  each  end  of  beam  is  found  by 
entering  the  diagram  with  the  unit  shear  at  the  support  and  the  clear  span  in  feet, 
and  following  the  directions  of  the  arrows  to  the  upper  left  hand  part  of  the  diagram. 
Note  that  Diagram  37  is  made  for  U-stirrups  only  with  the  exception  of  the  K-in. 
W-stirrup  which  has  a  total  cross-sectional  area  equal  to  the  %6-in.  square  U-stirrup. 
The  number  of  W-stirrups  required  in  any  given  case  will  be  one-half  the  number  of 
U-stirrups  of  the  same  size. 

Diagram  38  gives  the  distance  (I')  from  the  face  of  support  to  the  point  where  v  = 
40  Ib.  per  sq.  in.,  beyond  which  no  stirrups  are  required. 

Diagram  39  is  used  for  locating  the  stirrups  in  the  beam.  It  is  so  constructed  that 
if  any  one  of  the  horizontal  light  lines  is  assumed  to  pass  through  the  face  of  the  sup- 
port and  the  top  line  marked  "center  of  span"  is  assumed  to  pass  through  the  center 
of  span,  the  intermediate  light  lines  will  divide  the  triangular  shear  diagram  into  equal 
areas  and  the  heavy  lines  will  pass  through  the  centers  of  gravity  of  these  areas.  The 
heavy  lines  therefore  represent  the  location  of  the  stirrups. 

A  convenient  scale  is  placed  with  the  zero  on  the  fine  line  marked  with  a  number 

corresponding  to  Ns.     The  scale  is  then  rotated  until  it  reads—  (in  inches)  at  the  top 

z 

line  (center  of  span  line).  The  distances  from  the  face  of  support  to  the  heavy  lines 
are  then  read  directly  from  the  scale,  stopping  when  I'  is  reached.  One  side  of  a 
triangular  engineers'  scale  may  be  used  for  all  ordinary  cases. 

Required  to  space  %-4n.  round  U-stirrups  in  a  beam  10  in.  wide  and  of  IS-ft.  clear 
span,  having  a  shear  at  the  support  of  118  Ib.  per  sq.  in. 

From  Diagram  37 

Ns  =  12 
From  Diagram  38 

I'  =  71  in. 

Placing  scale  on  Diagram  39  to  read  zero  at  Ng  =  12  and  108  on  line  marked 
"center  of  span,"  the  distances  in  inches  from  the  face  of  support  to  the  points  where 
stirrups  should  be  placed  are:  2^,  7,  12,  17,  2%  28^,  35,  42,  50,  59,  and  70.  This 
theoretical  spacing  will  usually  be  modified  by  practical  considerations,  such  as  the 
maximum  spacing  allowable  for  the  depth  of  beam.  The  spacing  of  stirrups  should 
not  be  greater  than  about  one-half  the  beam  depth. 

Beams  with  Concentrated  Loads 

Diagrams  40  and  41  may  be  used  to  find  the  theoretical  spacing  of  stirrups  for 
beams  with  concentrated  loads,  the  concrete  assumed  to  take  one-third  of  the  total 
shear.  Diagram  40  is  based  on  unit  shear  and  Diagram  41  on  total  shear.  The 
spacing  of  stirrups  will  ordinarily  be  made  uniform  between  load  concentrations. 

83 


SHEAR 
REINFORCEMENT 


DIAGRAM  36 


UNIT  SHEAR  AND  BOND  STRESS 
j  =  0.875 


-.  \L        n,     V 
bid        u  ZQJZ 


?& 


^? 


#^^ 


DIAGRAM  37 


SHEAR 
REINFORCEMENT 


STIRRUPS  FOR  UNIFORMLY  LOADED  BEAM 
fa=16,000 


Unit  shear  at  support 


AT,  =  Total  Number  of 
Stirrups  in  Each  End 
of  Uniformly  Loaded 
Beam  From  Support 
to  Center — Concrete 
Taking  One-third  of 
Total  Shear. 
vbl 


6AJ, 
fa  =  16,000  Ih.  per  sq.  in. 


85 


SHEAR 
REINFORCEMENT 


DIAGRAM  38 


UNIFORMLY  LOADED  BEAMS 
LENGTH  OF  BEAM  REQUIRING  SHEAR  REINFORCEMENT 


Clear  span   in  feet.    •£. 


86 


DIAGRAM  39 


SHEAR 
REINFORCEMENT 


DIAGRAM  FOR  LOCATING  STIRRUPS 

IN 
UNIFORMLY  LOADED  BEAMS 


^•-Center  of  span 

^ 

I 

<5 

I 

vv 

2 

3 

4- 

T 

5 

^ 

r 

6 

1 

7 

T 

Q 

1 

9 

i 

10 

II 

1 

j 

f  \ 

\z 

\ 

I 

/ 

13 

N 

=  1 

14 

87 


SHEAR 
REINFORCEMENT 


DIAGRAM  40 


SPACING  OF  U-STIRRUPS 

CONCRETE  TAKING  ONE-THIRD  OF  TOTAL  SHEAR 
fs  =  16,000 


DIAGRAM  41 


SHEAR 

REINFORCEMENT 


SPACING  OF  STIRRUPS 

CONCRETE  TAKING  ONE-THIRD  OF  TOTAL  SHEAR 
fs=  16,000 


89 


SECTION  7 
COLUMNS 

The  following  tables  of  safe  loads  on  columns  are  based  on  the  requirements  of  the 
respective  codes  in  regard  to  maximum  and  minimum  percentages  of  vertical  steel  and 
spiral,  and  also  on  such  practical  considerations  as  the  minimum  spacing  of  vertical 
steel.  The  number  of  rods  in  the  square  cored  columns  is  limited  to  eight  because 
every  rod  should  be  tied  back  into  the  column  by  the  binders  and  it  is  ordinarily  better 
practice  to  iise  a  spiraled  column  if  more  than  eight  rods  are  found  necessary. 

The  tables  for  round  cored  hooped  columns  are  so  complete  that  it  should  be 
possible  to  select  a  satisfactory  design  for  any  condition  of  concentric  loading  without 
additional  computation.  The  values  of  safe  loads  given  in  Tables  35  to  42  inclusive 
are  based  on  the  percentages  of  spiral  listed  and,  if  desired,  another  spiral  of  equal 
volume  may  be  substituted  from  Table  46. 

Diagrams  42  and  43  will  be  found  valuable  for  determining  building  column  loads 
for  preliminary  work. 

For  the  design  of  columns  which  are  eccentrically  loaded,  see  Section  8.  Diagrams 
for  the  design  of  round  columns  subjected  to  bending  and  direct  stress  have  been 
constructed  and  are  published  here  for  the  first  time. 

What  size  of  square  cored  column  and  what  amount  of  longitudinal  steel  will  be  re- 
quired to  support  a  centratty  applied  load  of  200,000  lb.,  assuming  the  recommendations  of 
the  Joint  Committee  to  govern?  Ratio  of  unsupported  length  of  .column  to  column  side  is 
less  than  15. 

Tables  21,  22  and  23  show  the  following  possible  designs: 

2000-to.  concrete. 

(  6-134  in-  square 
22-m.  column  So,,/. 

I  8-1  Y%  in.  square 

( 6-1  in.  square 
23-in.  column  \  0  -  .  , 

I  8-1  in.  round 

2500-&.  concrete. 


-         n.  square 
20-in.  column  <        ,*  . 

18»1>B  in.  square 

f  6-1  in.  square 
21-m.  columns  _  .,  . 

I  8-1  in.  round 

3000-&.  concrete. 

19-in.  column  {  8-1  ^  in.  round 


-       n.  square 
20-m.  column  <  „  '  . 

(  6-1  in.  round 

Lateral  ties  must  be  used  of  not  less  than  34  in.  in  diameter  and  spaced  not  over 
12  in.  apart.  For  %-in.  rods  the  spacing  should  never  be  more  than  10  in. 

What  size  of  round  column  and  what  amount  of  longitudinal  steel  will  be  required  by 
the  Joint  Committee  Recommendations  to  support  a  load  of  1,100,000  lb.?  A  3000-lb. 
concrete  is  to  be  used  with  1  %  of  spiral  reinforcement.  Unsupported  length  of  column  is 
less  ttian  10  diameters. 

91 


COLUMNS 

From  Table  34,  page  114,  it  is  found  that  a  37-in.  round  column  with  33-in. 
core,  and  with  fourteen  l^-in.  square  longitudinal  rods  will  safely  support  a  load  of 
1,105,000  Ib. 

Table  47  shows  that  a  spiral  of  7/0  gage  and  2%-m.  pitch  will  give  1  %  of  reinforce- 
ment; or  that  a  %-in.  spiral  may  be  used  with  2%-in.  pitch.  Table  46,  page  188,  gives 
other  satisfactory  sizes  and  pitch  of  spirals  to  obtain  the  required  1%  of  spiral  re- 
inforcement. This  table  also  gives  the  weight  in  pounds  per  foot  of  column  for  each 
spiral.  Table  45  gives  the  volume  and  weight  of  columns  per  foot  and  Table  44  gives 
the  weights  of  column  rods  per  foot. 

What  would  be  the  design  of  the  column  of  the  preceding  problem  assuming  the  American 
Concrete  Institute  recommendations  to  govern? 

A  number  of  satisfactory  designs  may  be  taken  from  Table  37.  One  possible 
design  is  to- use  a  37-in.  column  with  33-in.  core  and  a  spiral  of  7/0  gage,  2^-in.  pitch, 
sixteen  IJ^-in.  round  longitudinal  rods. 

Reduction  Formula  for  Long  Columns. — Where  long  columns  must  be  used,  the 
reduction  which  follows,  taken  from  the  Los  Angeles  Building  Code,  may  be  employed 
in  the  design  of  columns  whose  unsupported  length  (1}  is  between  15  and  30  times  the 
least  dimension  of  effective  section  (d).  Let  r  represent  the  quantity  by  which  the 

working  stress  for  columns  with  -i  less  than  15  should  be  multiplied  to  give  a  working 
stress  which  may  be  used  for  long  columns.     Then 

r-l.6-H.fi 


92 


TABLE  21 


COLUMNS 


^  .Gi'umn  size    J 


SQUARE  CORED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Max. 


/unsupported  length\ 


side 


15 


2000- Ib.  concrete 
1:6  mixture 
n  =  15 
ft=450 


"of* 

column 
(.inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods                                                   Round  rods 

X 

H       H 

1 

1H     IK       K       H 

H        i 

IK 

IK 

12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

8 
9 
10       . 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

4 
4 

4 

6 

8 

8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

6 
8 

4 
6 
8 

6 

8 

38.6 
46.3 

i  54.8 
i  59.7 

;     64.7 

64.3 
69.2 
1  74.1 

74.6 
79.5 
84.5 

'90^8 
i  95.7 

102.9 
107.9 

iie.6 

120.9 
134.9 
i49.7 

43.0 
50.6 

59.2 
66.3 

36.5 
44^2 

52.7 
56.6 
60.4 

62.2 
66.0 
69.9 

"76  A 
80.2 

87.6 
91.5 

103.6 

40.0 
47.6 

56.2 
61.7 
67.2 

65.6 
71.1 
76.7 

76.0 
81.5 
87.0 

87.2 
92.7 
98.3 

i04.9 
110.4 

44.0 
51.6 

60.2 
67.7 

69.6 
77.2 
84.8 

80.0 
87.5 
95.1 

91.2 
98.8 
106.4 

103.4 
110.9 
118.5 

116.4 
124.0 
131.6 

56.2 
64.8 

74.2 
84.1 

84.6 
94.5 

95.8 
105.7 
115.6 

108.0 
117.9 
127.8 

121.0 
130.9 
140.8 

135.0 
144.9 
154.8 

149.8 
159.7 
169.6 

70.1 
79.5 
89.9 

101.1 
113.6 

113.3 
125.7 

126.3 
138.8 
151.3 

140.3 
152.8 
165.3 

155.1 
167.6 
180.1 

170.9 
183.3 
195.9 

187.5 
200.0 
212.5 

205.1 
217.5 
230.1 

95.7 
107.0 

119.1 
134.6 

132.2 
147.6 

146.1 
161.6 
177.1 

161.0 
176.4 
191.9 

176.7 
192.2 
207.7 
193.4 
208.8 
224.3 

210.9 
226.4 
241.9 

229.4 
244.8 
260.3 

248.7 
264.2 
279.7 

284.4 
299,9 

305.6 
321.1 

327.6 
343.1 

350.6 
366.0 

55.7 
64.3 

70.2 

68.6 
75.7 

82.8 

79.0 
86.1 
93.2 

90.2 
97.3 
104.4 

102.4 
109.5 
116.6 

115.4 
122.5 
129.6 

i36.5 
143.6 

ioi.3 
158.4 

73.7 
83.4 

79.7 

84.1 
93.7 

95.3 
105.0 
114.6 

107.5 
117.1 
126.8 

120.5 
130.2 
139.8 

134.5 
144.1 
153.8 

149.3 
159.0 
168.6 

90.0 

96.1 

101.3 
113.9 

113.4 
126.0 

107.9 

115.4 

i 

120.1  127.6 
136.0  

126.5 
139.1 
151.7 

140.4 
153.0 
165.6 

155.3 
167.9 
180.5 

171.0 
183.6 
196.2 

187.7 
200.3 
212.9 

205.2 
217.8 
230.4 

133.1 
149.1 

147.1 
163.0 
179.0 

161.9 
177.9 
193.8 

177.7 
193.6 
209.6 

194.3 
210.3 
226.2 

211.9 
227.8 
243.8 

230  3 

140.6 

117.9 
123.5 

154.6 
174.3 

116.7 

131.9 
137.4 

137.9 
145.5 

i52'.8 
160.4 

169.4 
189.1 

185.2 
204.9 
224.6 

201.8 
221.5 
241.2 

219.4 
239.1 

258.8 

237  8 



i52.3 

::::: 

167.1 
174.2 

174.7 
184.4 

168.5175.5 
176.1  185.4 

168.0 

191.4 
201.0 

185.2  192.1 
192.8202.0 

190.8 



.  .  208.9 
208.4218.6 

209.7 
219.6 

210.3 

227.4 
237.0 

236.3 
248.9 

246.3 
262.2 

249.7 
265.6 
281.6 

285  '.9 
301.8 

257.5 
277.2 

257.2 
276.9 
296.6 

277.4 
297.1 
316.8 

298.6 
318.3 
338.0 

320.6 
340.6 
360.0 

363.3 
383.0 

228.1 
238.0 

236.0 
248.5 

226.8 

228.8 

255.6 
268.2 

275  '.9 

288.5 

255.3 
267.9 

275.6 
288.1 

296.7 
309.3 

33i'.3 
354.3 



256.4 





257.4 
277  ".6 

i" 

276  '.6 

i  .  .  .  . 

297.0 
309.6 

307.0 
323.0 

297.8 



::•;• 

;;;;; 

298.8 
320  '.8 

33i'.7 

329.1 
345.0 

352.0 
368.0 

354.6 



93 


COLUMNS 


TABLE  22 


SQUARE  CORED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


2500-lb.  concrete 
1:4%  mixture 
n  =  12 
fc=565 


Max. 


/unsupported  length^ 


side 


15 


Size 
of 
column 
(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

y* 

1 

IK 

IK 

H 

H 

V* 

1 

IK 

IK 

12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
20 
27 
28 
29 
30 

8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

4 
4 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

: 

i 

4 

6 
8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

6 
8 

45.9 
55.5 

!  66.2 
71.1 
75.9 

1  78.1 
!  82.9 
•  87.8 

91.1 
95.9 

;100.8 

50.1 
59.8 

70.5 
77.5 

82.4 
89.3 
96.3 

95.3 
102.3 
129.3 

109.5 
116.5 
123.5 

124.7 
131.7 
138.7 

141.1 
148.1 
155.1 

ies'.e 

172.6 
184  3 

64.8 
75.5 

! 

43.8 
53.4 

64.1 
67.9 
71.8 

76.0 
79.8 
83.6 

'92  '.8 
96.6 

ioe>'.9 

110.7 

47.1 
56.8 

67.5 
73.0 

78.5 

79.4 
84.8 
90.3 

92.3 

97.8 
103.3 

106.5 
112.0 
117.5 

i27!  2 
132.7 

51.1 
60.7 

71.5 

78.9 

83.3 
90.8 
98.3 

96.3 
103.8 
111.3 

110.4 
117.9 
125.4 

125.7 
133.2 
140.6 

142.1 
149.6 
157.0 

i<37\i 
174.5 

185'  7 

65.3 
76.0 

87.9 
97.7 

100.9 
110.7 

115.0 
124.8 
134.5 

130.3 
140.0 
149.8 

146.7 
156.4 
166.2 

164.2 
173.9 
183.7 

182.8 
192  6 

81.2 
93.1 
106.1 

120.2 
132.6 

135.5 

147.8 

151.8 
164.2 
176.6 
169.4 
181.7 
194.1 

188.0 
200  4 

111.9 
126.0 

141.3 
156.5 

157.6 
172.9 

175.2 
190.4 
205  .  7 

193.8 
209   1 

81.4 

87.4 
96.9 

93.2 

100.4 
109.9 

106.2 

112.8 



114.5 
124.0 
133.6 

129.8 
139.3 
148.8 
146.2 
155.7 
165.2 

163  .  7 
173.2 

182.7 

182.3 
191   8 

120.4 
132.8 

135.6 
148.0 

127.0 

142.2 
157  9 

134.3 
149.6 

J110.1 
1114.9 

i25.3 
130.2 

i4i'.7 

146.6 

iei'.i 

126.0 

152.0 
164.4 
176.9 

169.5 
181.9 
194.4 

188.2 
200  6 

158.6 
174.3 

176.1 
191.8 
207.6 

194.8 
210.5 

166.0 

183.5 
202.9 

202.1 
221   6 

l42'.4 

143.6 
149.1 

iei  '.  i 

166.6 

182.7 

191.3 

204  '.6 
211.0 

201.4 

2ii'.6 
22}.  1 

213.0 

207.9 
220.4 
232.8 

228.8 
241.3 
253.7 

250  9 

226.2 

214.5 
230.3 
246.0 

235.4 
251.2 
266.9 
257  5 

185.3 

193.2 

202.3 

212.7 

207.8 
220.1 
232.5 

228.7 
241.0 
253.4 

250.7 
263.1 
275.4 

224.3 

213.6 

228.8 
244.1 

234.5 
249.7 
265.0 

256.5 
271.8 
287.0 

279.7 
294.9 
310.2 

304.0 
319.2 
334.5 

344.7 
359.9 

371.2 
386.5 

398.9 
414.1 

427.7 
443.0 

221.9 
241.3 
260.8 

242.8 
262.2 
281.7 

264  8 

'.'.'.'.'. 

205  '.6 

205.5 
213.0 

226  '.4 
233.9 

212.4 
222.1 

233.3 
243.0 

1  

231  '.9 

232.5 
242.0 

254.6 
264.1 

277  '.7 
287.2 

263.3 
275.7 

286  '.5 
298.9 

273.2 
288.9 

280.6 
296.4 
312.1 

304.9 
320.7 
336.4 

284.3 
303.7 

288.0 
307.4 
326.9 

312.3 
331.7 
351.2 

337.7 
357.2 
376.6 

364.3 
383.7 
403.1 

392.0 
411.4 
430.8 

440.2 
459.6 

255.9 

255.3 
265.1 

1  

254.0 
277'.! 

\  



279  .  i 

278.5 
288.2 

286.2 
298.6 

310.5 
322.9 

336.0 
348.3 

362.5 
374.9 

402  '.6 
43i.4 

3ii.5 

310.8 
323.2 

312.5 

336.2 
348.6 

362  '.7 
375.2 

346.1 
361.8 

372  '.6 
388.4 

400  '.3 
416.1 

429  .1 
444.9 

337.6 
363  .  5 

337.9 
364  '.5 
392  '.2 

1  



402  '.9 
43i'.7 









94 


TABLE  23 


COLUMNS 


,  Cotumnsizf 


SQUARE  CORED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


/unsupported  length\ 

Max.  [  -  —  T3  —  I  =  15 

V  side  / 


3000-  Ib.  concrete 
1:3  mixture 
n  =  10 
fc=675 


Size 
of 
column 

(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

K 

H 

H 

1 

IX 

IK 

% 

y* 

H 

1 

IK 

IK 

12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

4 

4 

4 
6 

8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 

6 
8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

6 

8 

52.7 
64.2 

78.0 
81.7 
86.5 

91.2 
95.9 
100.7 
'106.7 

111.4 
116.2 

'i28'.3 
133.1 

i46.5 
1151.3 

iee'.i 

170.9 

igi'.s 
2i4'.i 

56.9 
68.3 

81.2 
86.0 

50.7 
62.1 

75.0 

78.7 
82.4 

89.1 
92.9 
96.6 

i08.4 
112.1 

i25'.  3 
129.0 

53.9 
65.4 

78.2 
83.6 
89.0 
92.4 
97.8 
103.2 

107.9 
113.3 
118.7 

124.8 
130.2 
135.6 

57.8 
69.3 

82.1 
89.4 

96.3 
103.6 
110.9 

111.8 
119.1 
126.4 

128.7 
136.0 
143.3 

146.9 
154.2 
161.5 

166.5 
173.8 
181.1 

73.8 
86.6 

100.8 
110.3 

116.3 
125.8 

133.2 
142.7 
152.3 

151.4 
160.9 
170.5 

171.0 
180.5 
190.1 
191.9 
201.4 
211.0 

214.6 
223.7 
233.3 

91.7 
105.7 
121.4 

138.2 
150.3 

156.5 
168.5 
180.6 

176.0 
188.1 
200.2 

197.0 
209.0 
221.1 
219.2 
231.3 
243.4 

242.9 
254.9 
267.0 

267.8 
279.9 
292.0 

294.2 
306.2 
318.3 

127.0 
143.9 

162.1 
177.0 

181.7 
196.6 

202.6 
217.5 
232.4 

224.9 
239.8 
254.7 

248.5 
263.4 

278.3 

273.5 

288.4 
303.3 

299.8 
314.7 
329.6 

327.5 

73.3 
86.1 

91.8 

95.3 
102.2 
109.0 
110.9 
117.7 
124.5 

127.7 
134.6 
141.4 

146.0 
152.8 
159.6 

165.5 
172.4 
179.2 

i93.3 
200.1 

2is'.6 
222.4 

100.3 
109.6 

106.0 

115.8 
125.1 

121.5 

128.0 



132.7 
142.0 
151.3 

150.9 
160.2 
169.5 

170.5 
179.8 
189.1 

191.4 
200.7 
210.0 

213.7 
223.0 
232.3 

138.4 
150.5 

144.8 

152.0 

156.6 
168.8 

163.1 
178.4 

170.3 

148.4 
153.8 

ies'.o 

173.4 

147.2 

iee'.s 

176.2 
188.3 
200.5 

197.1 
209.3 
221.4 

219.4 
231.5 
243.7 

243.0 
255.2 
267.3 

268.0 
280  1 

182.6 
198.0 

203.6 
218.9 
234  3 

189.8 

210.8 
229.8 

188.9 
194.3 

194.7 
202.0 

225.8 
241.2 
256.6 

249.5 
264.8 
280.2 

274.4 
289  8 

233.0 
252.0 

256.7 
275.7 
294.6 

281.6 
300  6 

217.0 
224.3 

216.6 

::::: 

239.2 
246.0 

246.6 
255.9 

27i   6 

240.2 

240.6 
247.9 

247.3 
256.9 

i 

265.6 
272.9 

299  '.2 

272.3 
281.9 

298  '.6 
308.2 

:;!"!! 

271.0 
297  '.3 

280.9 

297.9 
307.2 

325  '.6 
334.9 

363  '.9 

292.3 

294,3 
306.5 
318.6 

334.  i 
346.3 

363  '.2 
375.3 

305.2 

300.8 
316.1 
331.5 

328.4 
343.8 
359.2 

357.5 
372.8 
388.2 

319.6 

308.0 
327.0 
345.9 

335.5 
354.6 
373.6 

364.7 
383.7 
402.6 

395.0 
414.0 
433.0 

426.8 
445.8 
464.7 

459.8 
478.8 
497.8 

513.3 
532.2 

326.3 
335.9 

364  '.9 
395.3 

333.9 
346.0 

362  '.9 
375.0 

393.3 
405.4 

425.0 
437.1 

470  '.2 
504  '.6 

342.3 
357.3 

356.5 
371.4 
386.3 

401.8 
416.7 

433.5 
448.4 

466.3 
481.5 

501.0 
515.9 



325.0 

326.9 

::::: 

|  

••••• 

•  •  •  •  • 

394  '.3 

393.5 
405.7 

403.2 
418.6 

434  '.9 
450.3 

::::.: 



426.6 

425.3 
437.4 

i  

427.0 
460.  i 

'.'.'.'.'. 



••••• 

470  '.5 
504.9 

468.0 
483.4 

502.4 
517.8 

95 


COLUMNS 


TABLE  24 


SQUARE  CORED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS 

AND 


NEW  YORK  CITY  BUILDING  CODE  REQUIRE- 
MENTS 

2000  -Ib.  concrete                               P  =Afc[l  +  (n-l)p] 
1:6  mixture                              ,_       (unsupported  length\ 
n  =  15                                         Max.(-                               -J  =15 

fc=500 

(  Column  cize 

j? 

sksSs^ 

ip.^ 

«  iCV.-.-.--o-.-.-:i  J 

^liftl 

x  ConrSize  > 

Size 
of 
column 
(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

'H 

y* 

1 

1H 

IK 

% 

H 

14 

i 

1H 

iy* 

12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

4 
4 
4 

e 

8 

4 
6 

8 

4 
6 

8 

4 
6 

.8 

4 
6 

8 

4 
6 

8 

4 

6 

8 

4 

6 
8 

4 
6 

8 

4 

6 

8 

4 

6 

8 

4 
6 

8 

4 

6 

8 

4 

6 

8 

4 
6 

8 

4 
6 
8 

4 
6 

8 

42.9 
51.4 

60.9 
66.4 
71.9 

71.4 
76.9 
82.4 

82.9 
88.4 
93.9 

95.4 
'100.9 
106.4 

108  9 

1  14  .  4 
119.9 

123.4 
128.9 
134.4 

138.9 
144.4 
149.9 

155.4 
160.9 
166.4 

178.4 
183.9 

igeig 

202.4 

2ie'.4 

221.9 

236  '.9 
242.4 

47.8 
56.3 

65.8 
73.6 

40.6 
49.1 

58.6 
62.9 
67.2 

69.1 
73.4 

77.7 

80.6 
84.9 
89.2 

93.1 
97.4 
101.7 

106.6 
110.9 
115.2 

121.1 
125.4 
129.7 

146  '.9 

145.2 

i57.4 
161.7 

174  '.9 
179.2 

i93.'4 
197.7 

44.4 
52.9 

62.4 
68.6 
74.7 

72.9 
79.1 
85.2 

84.4 
90.6 
96.7 

96.9 
103.1 
109.2 

110.4 
116.6 
122.7 

124.9 
131.1 
137.2 

140.4 
146.6 
154.7 

156.9 
163.1 
169.2 

174.4 
180.6 
186.7 

199.  'i 
205.2 

48.8 
57.3 

66.8 
75.3 

77.3 

85.8 
94.2 

88.8 
97.3 
105.7 

101.3 
109.8 
118.2 

114.8 
123.3 
131  .  7 

129.3 
137.8 
146.2 

144.8 
153.3 
161.7 

161.3 
169.8 
178.2 

178.8 
187.3 
195.7 

197.3 
205.8 
214.2 

216.8 
225.3 
233.7 
237.3 
245.8! 
254.2 

267.3 
275.7 

289  '.8 
298.2 

sis.  3 

321.7 

62.5 
72.0 

82.5 
93.5 

94.0 
105.0 

106.5 
117.5 
128.5 

120.0 
131.0 
142.0 

134.5 
145.5 
156.5 

150.0 
161.0 
172.0 

166.5 
177.5 
188.5 

184.0 
195.0 
206.0 

202.5 
213.5 
224.5 

222.0 
233.0 
244.0 

242.5 
253  .  5 
264.5 

264.0 
275.0 
286.  0; 

286.5* 
297.5 
308.5 

310.0 
321.0 
332.0 

334.5 
345.5 
356.5 

77.8 
88.3 
99.8 

112.3 
126.3 

125.8 
139.8 

140.3 
154.3 
168.2 

155.8 
169.8 
183.7 

172.3 
186.3 
200.2 

189.8 
203.8 
217.7 

208.3 
222.3 
236.2 

227.8 
241.8 
255.7 

248.3 
262.3 
276.2 

269.8 
283.8 
297.7 

292.  31 
306.3 
320.2 

315.8 
329.8; 
343.7 

340.3 
354.3 
368.2 

365.8 
379.8 
393.7' 

106.4 
118  .9 

132.4 
149.5 

146.9 
164.0 

162.4 
179.5 
196.7 

178.9 
196.0 
213.2 

196.4 
213.5 
230.7 

214.9 
232.0 
249.2 

234.4 
251.5 
268.7 

254.9 
272.0 
289.2 

276.4 
293.5 
310.7 

298.9 
316.0 
333.2 

322.4 
339.5 
356.7 

346.9 
364.0 
381.2 

372.4 
3S9.5 
106.7 

61.9 
71.4 

78.0 

!  76.3 
84.1 
92.0 

87.8 
95.6 
103.5 

100.3 
108.1 
116.0 

113.8 
121.6 
129.5 

128.3 
136.1 
144.0 

143.8 
151.6 
159.5 

160.3 
168.1 
176.0 

177.8 
185.6 
193.5 

196.3 
204.1 
212.0 

215.8 
223.6 
231.5 

236.3 
244.1 
252.0 

81.9 
92.7 

88.5 

93.4 
104.2 

100.0 

105.4 

105.9 
116.7 
127.4 

119.4 
130.2 
140.9 

133.9 
144.7 
155.4 

149.4 
160.2 
170.9 

165.9 
176.7 
187.4 

183.4 
194.2 
204.9 

201.9 
212.7 
223.4 

221.4 
232.2 
242.9 

241.9 
252.7 
263.4 

263.4 
274.2 
284.9 

285.9 
296.7 
307.4 

309.4 
320.2 
330.9 

344  .  7 
355.4 

112.5 
126.5 

126.0 
ITO.O 

119.9 

128.3 

133.4 
151.2 

141.8 

140.5 
154.5 
168.5 

156.0 
170.0 
184.0 

172.5 
186.5 
200.5 

190.0 
204.0 
218.0 

208.5 
222.5 
236.5 

228.0 
242.0 
256.0 

248.5 
262.5 
276.5 

270.0 
284.0 
298.0 

292.5 
306.5 
320.5 

316.0 
330.0 
344.0 

340.5 
354.5 
368.5 
366  0 

147.9 
165.7 

156.3 

163.4 
181.2 
198.9 

179.9 
197.7 
215.4 

197.4 
215.2 
232.9 

215.9 
233.7 
251.4 

235.4 
253.2 
270.9 

255.9 
273.7 
291.4 

277.4 
295.2 
312.9 

299.9 
317.7 
335.4 

323.4 
341.2 
358.9 

347.9 
365.7 
383.4 
373  4 

171.8 
193.6 

188.3 
210.1 

205.8 
227.6 
249.5 

224.3 
246.1 
268.0 

243.8 
265.6 
287.5 

264.3 
286.1 
308.0 

285.8 
307.6 
329.5 

308.3 
330.1 
352.0 

331.8 
353.6 
375.5 

356.3 
378.1 
400.0 
381    8 

2i7'.2 
237  '.7 
259.2 
28i  .-7 

218.6 
224.7 

239.  i 
245.2 

260  .  6 
266.7 

283  '.i 
289.2 

263  '.9 
286  '.4 
309.9 
334  '.4 

265.6 
273.5 

288  '.1 
296.0 

3ii.6 
319.5 

336!  1 
344.0 

:::: 

3i2'.7 

.... 

337  '.2 

337.8 
346.2 

36i.6 
369.5 

376.2386.6|391.2403.6 
380.9394.0,408.9  425.5 

363.3 
371.7 

371.0 
382.0 

362.7 

96 


TABLE  25 


L  Colur^n  sira    J 


COLUMNS 


SQUARE  CORED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
AMERICAN  CONCRETE  INSTITUTE 
RECOMMENDATIONS 


Max. 


/unsupported  length^ 


side 


15 


2500 -Ib.  concrete 
1:4%  mixture 
n=12 
f c  =  625 


Size 
of 

column 
(inches) 


Size 

of  • 

core 

(inches) 


Number 

of 
rods 


Square  rods 


1    I  IK  I  IK 


Round  rods 


K 


12 

13 

14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 


8 

9 

10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 


50. 7j 

61.4 

73.2 

78.6 
84.0: 

86. 4J  91.1 
91.7    98.8 


55.5 
66.1 

78.0 
85.7 


71.7 
83.6 


107.2 


97.5 


103.1 


97.1  loee  .... 

100.7105.51111.1 
106.1  113.2121.6 
111.5  120  9 


117.5124.8  . 


116 
121 

127 

|  133 

;  138 

I  144 

151 

156 

162 

170, 

176, 

181. 

191. 
196. 
202. 


218 
224 


241 
247 


4  121 
7  128 
1  136 

2!l38 
6;  145 
0153 

4'  156 
7  163 

1171 

7|175. 
11183. 
5190. 

4J196. 
7203. 
211. 

218. 
6225. 
0233. 

241. 

.7248. 

256. 


48.4 
59.1 

70.9 
75.2 
79.4 

84.1 
88.3 
92.5, 


52.2 
62. 8! 
74.7J 


56.5 
67.2 
79.0 


80.71  87.3 
86.8J 

87. 8i  92.2 
93.9  100.4 
99.9  108.7 


1         IK      IK 


72.2 
84. l' 


89.8 


97.2103.0 
108.0 


98.4  102.2  106.5  111.6117.3 
102.7108.2  114.8122.4 
106.9  114.3  123.1 


.l'l26.7  132 
.8137.2146 
.6J147.7  . .. 
.0!l43.6il50.o'l57.3i165.5  130.9 

.7154.1163.8174.7 135.2 

41164.6 | 139.4 


1  161.7 

8172.2 

6182.7 

181.1 


2  191 
202 

201 
8:212 
6J222 


1  140.4  148.6   114.1  117 

9 i  118.3  123 

.| i !  122.5129 

134 
140 
146 


8  122.2J127.2 

9  130.4  138.0 
9!138.7148.8 


123.8 


133.0  139.4 
146.6 


168. 
181. 
195. 

187. 


l'l75.4183 
9  192.8  ... 
6'.. 


. 6 


5  194.8203 
6201.3212.2224 
0^29.6, 


266.1 
271.5 


291.7 
297.1 


352.1 
38i' 


7234 
4244 

l!246, 

8257. 
6267 


215. 

7 
2|221 

7J235.6250.2 

61230 
1  243 
6257 


1215. 4^223. 
9232.8J245. 


265.5271 
273.2281 
280.9:292 

291.1296 

298.8307 

306.6317 

.J323 


325.7,334 
324.0333.4344 


7,243 
2!266 
.71280, 

.1277, 
.6291, 
.  1  305 , 

.7303. 
.2316. 
.7,330. 

.6330. 
.1  343. 
.6357. 


0237.3245.5 
8:254.7267.0 
5272.1  288.4 

l'260.4268.6 
9277.8290.1 
6295.2311.6 


.351.7358 
353.8362.2371 
361.6372.7385 

.'381 

383  2391.6401 
5390.9402 


.1 


413.8422 
421.6432 

445   7  454 
453.4464 


415 


418 
2431 
.7445 

450 

463 

6|477 


5284 
3302 
OJ319 
11310 
9327. 
6345. 

0337. 

8354. 
5372. 

1365. 
9382. 
6,400. 

5!  394 . 
3*412. 
OJ429. 

T425. 
9442. 
6460. 

0457. 
8474. 
5:492. 


.8293.0 
.2314.5 
.6335.9 

.4318.6 
.8340.1 
.2.361.6 

s'345.5 
7'367.0 
1  388.4 

4373.6 
8  395 . 1 
2j416.6 

8403.0 
21424  5 
6J445.9! 

4433.6' 
8455.1 
2476.6 

3465.5 
7487.0 
1  508.4 


7  139 
7147 

8155 


149.1  152.8157 
9  165 
9  173 


. 

153.3  158 
157.5164 


172 

172.7  178 
176.9  184 

192 

193.3  198 
197.5204 


2  176. 
2184. 
3193. 

8197. 
9  205. 
9213. 


0144 
3!154 

6  165 
2162 
4  173 

7  183 

5181 
8192 
1  203 
2202 
4J213 
7223 


1149 
9  163 

7| 

2  168 
0181 
8  195 
6187 
4  201 
2.214 

2' 208 
0221 
8235 


.8156.3 
.5173.1 

.0  174.4 
.6191.3 

.31193.8 
.OJ210.6 
.7227.5 

,0!214.4 
.6231.3 
.3  248.1 


214.7219.0224.1  229.8!236.3 
215.2220.7|227.3234.9:243.5253.1 
219. 41226.8235.6245.71257.2  270.0 
242. 2247. 2^53. 0*259. 4 
238.3243.9250.4258.0266.6276  3 
242.5249.9  258. 7  268. 8280. 3J293.1 

266.5271.6277.3283.8 

268.2,274.8282.4  291.0300.6 
266.9  274 .3|283 .  l!293  .2  304 .7*317 .5 

!292.2297.2!303.0309.4 

293.9300.4308.0316.6:326.3 
292 .5  299 .9j308 .7  318 .8|330 .3  343 . 1 

324.r329.s'336.3 
334.91343.5353.1 
319.4326.8335.6345.71357.2370.0 


320.7327.3 


347 


.  348 
5354 


3S4 


414 


446 


9355 

I)  303 


.  384 
.3393 


.  415 
.9423 


.  447 
8455 


.  352 . 
.4  363. 
.7J373. 

.381. 
.8392. 
.1408. 
.!412. 
4423. 
7433. 

3454. 
6  465 . 


2358 
0371 

8J385 

6387. 
4401. 
2414. 

2,418. 
0|431. 
8445. 

.  449'. 
9463. 

7477. 


.0364.4 
.6381.3 
.3398.1 

.3(393.8 

.0410.6 
.7427.5 
.0424.4 
.6441.3 
.3458.1 

8456.3 
5473.1 
2490.0 


97 


COLUMNS 


TABLE  26 


SQUARE  CORED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 


AMJttKK 
I 

3000-lb.  concrete 
1:3  mixture                            „- 
7i  —  12                                         Max. 

f     750 

JAJN    UUJNUK..&J..&   1HS11J 

RECOMMENDATIONS 

P  =  Afc[l  +  (n  —  l)p] 
/unsupported  length\ 

U1H, 

15 

Cofumn  size 

•  &*£$£$]* 

siny 

!  j 

N, 

\                side               ) 

Size 
of 
column 
(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

K 

% 

1 

IK 

IK 

H 

K 

Vs 

i 

IK 

IK 

12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30      • 

8 
9 
10 

11 

12 
13 
14 
15 
10 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

4 
4 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 
8. 

4 
6 

8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

60.9 
73.6 

87.9 
94.3 
100.8 

103.6 
110.1 
116.5 

120.9 
127.3 
133.8 
139.6 
146.1 
152.5 

159.9 
166.3 
172.8 

181.6 
188.1 
194.5 

204.9 
211.3 

217.8 

229.6 
236.1 
242.5 

262.3 
268.8 

290.1 
296.5 

3i9'.3 
325.8 

350  '.i 
356.5 

66.6 
79.3 

93.6 
102.8 

86.0 
100.3 

58.1 
70.9 

85.1 
90.2 
95.3 

100.9 
105.9 
111.0 

118.1 
123.2 
128.3 

136.9 
141.9 
147.0 

157.1 
162.2 
167.3 

178.9 
183.9 
189.0 

207.2 
212.3 

23i'.9 
237.0 

258  '.2 
263.3 

285.9 
291.0 

320.3 

62.6 
75.3 

89.6 
96.9 
104.2 

105.3 
112.6 
119.9 

122.6 
129.9 
137.2 

141.3 
148.6 
155.9 

161.6 
168.9 
176.2 

183.3 
190.6 
197.9 

206.6 
213.9 
221.2 

231.3 
238.6 
245.9 

257.6 
264.9 
272.2 

292  '.6 
299.9 

32i'.9 
329.2 

67.8 
80.6 

94.8 
104.8 

110.6 
120.4 
130.4 

127.8 
137.8 
147.7 

146.6 
156.5 
166.4 

166.8 
176.8 
186.7 

188.6 
198.4 
208.4 

211.8 
221.8 
231.7 

236.6 
246.5 
256.4 

262.8 
272.8 
282.7 

290.6 
300.5 
310.4 

319.8 
329.8 
339.7 

350.6 
360.5 
370.4 

392  '.8 
402.7 

86.7 
100.9 

116.7 
129.6 

133.9 
146.9 

152.7 
165.6 
177.6 

172.9 
185.9 
198.8 

194.7 
207.6 
220.6 

217.9 
230.9 
243.8 

242.7 
255.6 
268.6 

268.9 
281.9 
294.8 

296.7 
309.6 
322.6 

325.9 
338.9 
351.8 

356.7 
369.6 
382.6 

388.9 
401.9 
414.8 

422.7 
435.6 

448.6 

457.9 
470.9 

483.8 

494.7 
507.6 
520.6 

107.8 
123.6 
140.8 

159.6 
176.0 

179.8 
196.1 

201.6 
218.0 
234.4 

224.8 
241.2 
257.7 
249.6 
266.0 
282.4 

275.8 
292.2 
308.7 
303.6 
320.0 
336.4 

332.8 
349.2 
365.7 

363.6 
380.0 
396.4 

395.8 
412.2 
428.7 
429.6 
446.0 
462.4 

464.8 
481.2 
497.7 

501.6 
518.0 
534.4 

539.8 
556.2 

572.7, 

148.5 
167.3 

187.5 
207.7 

209.3 
129.5 

232.5 
252  .  8 
273.0 

257.3 
277.5 
297.8 

283.5 
303.8 
324.0 

311.3 
331.5 
351.8 

340.5 
360.8 
381.0 

371.3 
391.5 
411.8 

403  .  5 
423.8 
444.0 

437.3 
457.5 
477.8 

472.5 
492.8 
513.0 

509.3 
529.5 
549.8 

547.5 
567.8 
588.0 

108.0 

109.3 
118.6 
127.9 

126.6 
135.8 
145.1 

145.3 
154.6 
163.9 

165.6 

174.8 
184.1 

187.3 
196.6 
205.9 

210.6 
219.8 
229.1 

235.3 

244.6 
253.9 

261.6 
270.8 
280.1 

289.3 
298.6 
307.9 

318.6 
327.8 
337.1 
349.3 
358.6 
367.9 

116.0 
128.7 

123.8 

133.3 

145.9 

141.0 

149.8 

152.0 
164.7 
177.3 

172.3 
184.9 
197.5 

194.0 
206.7 
219.3 

217.3 
229.9 
242.5 

242.0 
254.7 
267.3 

268.3 
280.9 
293.5 

296.0 
308.7 
321.3 

325.3 
337.9 
350.5 

356.0 
368.7 
381  -.3 

388.3 
400.9 
413.5 

422.0 
434.7 
447.3 

457.3 
469.9 
482.5 

506  '.7 
518.3 

544.9 
557.5 

159.8 
176.3 

168.5 

178.3 

180.0 
196.5 

188.8 
209.7 

198.6 

201.8 
218.3 
234.8 

225.0 
241.5 
258.0 

249.8 
266.3 

282.8 

276.0 
292.5 
309.0 

303.8 
320.3 
336.8 

333.0 
349.5 
366.0 

363.8 
380.3 
396.8 

396.0 
412.5 
429.0 

429.8 
446.3 
462.8 

465.0 
481.5 
498.0 

501.8 
518.3 
534.8 

540.0 
556.5 
573.0 

210.5 
231.4 

220.3 

233.8 
244.7 
275.5 

258.5 
279.4 
300.3 

284.8 
305.7 
326.5 

312.5 
333.4 
354.3 

341.8 
362.7 
383.5 

372.5 
393.4 
414.3 

404.8 
425.7 
446.5 

438.5 
459.4 
480.3 

473.8 
494.7 
515.5 

510.5 
531.4 
552.3 

548.8 
569.7 
590.5 

243.6 
269.3 

268.3 
294.1 

294.6 
320.3 
346.1 

322.3 
348.1 
373.9 

351.6 
377.3 
403.1 

382.3 
408.1 
433.9 

414.6 
440.3 
466.1 

448.3 
474.1 
499.9 

483.6 
509.3 
535.1 

520.3 
546.1 
571.9 

558.6 
584.3 
610.1 

351.0 
383  '.3 
4i7.6 

352.6 
359.9 

384  '.9 
392.2 

388  '.8 
422.5 

390.8 
400.1 

424  '.6 
433.9 

418.6 
425.9 

426.5 
436.4 

457  '.8 
494  .  5 

459.8 
469.1 

496  '.6 
505.9 

534.8 
544.1 

:  :  ;  ;  ; 

46i.2 

46i.8 
471.7 



497.9 

498.5 
508.4 

536  '.2 

536.8545.9 
546.7^58.8 

98 


TABLE  27 


COLUMNS 


Column  size 


SQUARE  CORED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


mixture 


=  12 


Size 

of 

column 
(inches) 


Size 
of 

core 
(inches) 


Number 

of 
rods 


Square  rods 


Round  rods 


H 


H  \  X  \  H 


1H 


12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
20 
27 
28 
29 
30 


8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25. 
20 


I  48. 7|  53.3 

j!  58.91  63.5    68.8 

i  70. 3!  54. 9!  80.2 
!  75.5!  82.3  .. 


82.9 


87.5!  92.8 
94.9  102  9 
93.2  102. 3| 

96.7  101.3106.6 
'101.9  108.7,116.7 
|107. 0116.1 

111.  7  116.3121.6 


86.4 


99 


112.8 


127 


116.9  123.7|131.7  141 
122.0  131.1141.8  ..  - 


8134 
0.  .. 


127.9 
133.1 
138.2 


142.7 


132.5  137. 8' 144 
139.9'l47.9  157 
147.3,158.0  .... 


0!151 

2  167 


145.3149.9  155.2161 
150.5  157.3  165.3  174 
155.6164.71175.4^87 

163. 9!  168.5;  173. 8  180 
•  169.1  175.9  183.9  193 
,184.21183. 3  194. 0206 


.0158. 
.7  .... 


183.7 188 
188.91195 
194. 0|  203 

'209 

209.9'216 
215.0J224 

.....231 
232.1  238 
237.2246 


3193 
7203 
1,213 

3214 
7224 
1  234 

5*236 
9246 
3257 


.6199 
.7213 
.8226 

.6!220 
.7234 

.8,247 

.  8*243 
.9  256 
.0269 


254.9260.21266 

255.5262.3270.3:279 
260.6269.7280.41292 


279.5284 

!280.1J286.9294 
285.2294.3305 

. .  .  310 
312.7320 


311.0320.1 


330 


,337 

339.71347 
338.0347.1357 

365 

367.9375 
366.2375.3386 


.8291 
.930-4 
.0317 

.6316 
.7330 
.8343 

.6343 
.7357 
.8370 
.8372 

.  .  401 


168 
6  185 

o'l87 
2203 
4220 

8(206 
0223 
2240 

8227 
0244 
2261 

01250 
2266 
4J283 

4273 
6290 
8306 

0298 
2314 
4  331 

s'323 
0340 


8350 
0367 
2384 

0379 
2395 
4412 

4408 


.4176. 
.1  ____ 

.o'l94. 
.7215. 

.8214. 
.5235. 
.2255. 

.8235 
.5256 
.2276 

.o'257 

.7278 
.4299 

.4381 

.1  301 
.8322 

o'sos 

.7326 
,4|347 
.s'331 
5352 
.2372 

.8358 
.4379 
.2399 

.0386 
.7407 
.4428 


46.5 
56.7 

68.1 
72.2 
76.2 

80.7 
84.7 
88.8 

94.5 
98.6 
102.6 

109.5 
113.6 
117.6 


50.1 
60.3 

71.7 
77.5 
83.3 

84.3 
90.1 
95.9  104 


98.1 
103.9 
109. 


125.7129 
129.8  135 
133.8,140 

143.1  146 
147.2152 

151.2  158 


54.3 
64.5 


75.9 
83.8 


69.3 
80.7 


.5  93.3 
.4  103.7 

. 4| 


102.3  107.1 

110.2  117.5 
7118.2 

117.3  122.1 


113 

118.9  125.2  132.5140.8! 

124.7133.2,142.9 


86.2 


98.8 


112.6  118.8 


127.6133.8 


..,,133. 5  138. 3  143. 8  150.0 
.1  141.4  148. 7J157.0  166.2 
.9  149.4  159.1 


.7 

!3|166.8  176.5ll87.5i 


150.9,155.7161.2167.4 
158.8I166.1!174.4  183.6 


.3 


185 
189 


206 
210 


!165.3'l69.5  174.3  179.8  186.0 
.8  171.  l|l77. 4  184.7  193.0202.2 
.8  176.9  185.4,195.1:206.1  218.4 


6190 
6196 

.206 
6212 
6227 


189. 
197. 


1  210. 
0|218. 
7226. 


3193 
2204 
7205.2214 

3215 
2225 
2235 


228 
232 


8234. 
8239. 


256 


2SO 


232  . 
240. 
248. 


5  237 
4247 
4258 


1  199 
5212 
9  225 

l' 220 
5233 
9,246 

3 '242 
7256 
i;269 


.6205.8 
.81222.0 
.9238.2 

.6226.8 
.8243.0 
.9,259.2 

.9^249.0 
.0265.2 
.1281.4 


? ::: 


397.3405.3414 


395.6404.7415.4 


427 


432 

427.9435.9J445 
435.3446.0458 


6425 
,8(441 

0439 
,2455 
4472 


1436 

,8457, 

01447 
7J467, 
4488. 


..   255.9260.7266.2272.4 

.  .  257.5  263  .8  271 . 1  279 .4  288.6 
.2263.3271.8^81.5292.5304.8 

..':....  280. 5285. 3i290. 8297.0 
.  .  282. H288. 4  295. 7^304.0313. 2 
.8  287. 9  296. 4  306.1  347. 1(329. 4 

.  .'311.l'316.6322.8 
.  .  307.9314.2321.5329.8339.0 
.6  313.7  322.2  331 .9  342.9  355.2 


333 


.  334 
6340 


361 


9341 
7349 


.9,377 

I 


8368 

'.  398.3406 

!  428 


.  429 
,9437 


.  338 
.2348 
.2358 

.1366 
,4376 
.4387. 

.395 

8406 
8416. 


4436 
4447 


1343 
5356. 
9369. 
3371. 
7385. 
1(398. 

7401. 
1414. 
5427. 


.6349.8 
.8366.0 
.5372.2 

.8378.0 
.0394.2 
.1410.4 

2407.4 
4  423 . 6 
5439.8 


.  431.8438.0 
7445.0454.2 
1  458.1  470.4 


99 


COLUMNS 


TABLE  28 


SQUARE  CORED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


2000-lb.  concrete 
1:  6  mixture 

71=15 

fc=400 


MaX.(lenff*h}=12 
\   side   I 


Size 
of 

column 
(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods                                                     Round  rods 

M 

H 

14 

1         IK 

IK 

H 

H 

K 

1 

IK 

IK 

12 

g 

4 

41  .2 

45  0 

39.3    42  3 

45.9 

13 

10 

4 

48.8 

52.6 

46.9 

49.9 

53.5 

14 

4 

57.2 

61  0 

65.6 

55  3 

57.3 

61.9 

66.0 

6 

6l'5 

67^3 

58^7 

63.2 

68.6 

g 

65.9 

62.2 

68.2 

15 

12 

4 

66.4 

70.2 

74.8 

80.0 

64.5 

67.5 

71.1 

75.2 

79.9 

70  7 

76.5 

67  9 

72  4 

77.8 

8 

75  .'l 

71  !4 

77  'A 

16 

13 

4 

76.4 

80.2 

84.8 

90.0 

96.0 

74.5 

77.5 

81.1 

85.2 

89.9 

95.1 

6              80   7 

86.5 

93.3 

77.9 

82.4 

87.8 

94.0 

8              1     HS  '  1 

92^8 

81  .4 

87.4 

94  .5 

17 

14 

4 

87.2 

91.0 

95.6 

100.8106.8 

85.3 

88.3 

91.9 

96.0 

100.7 

105.9 

6           !    91.5 

97.3 

104.1 

88.7 

93.2 

98.6 

104.8 

8           !   95.9 

103.6 

92.2 

98.2 

105.3 

18 

15                      4              99.8 

102.6 

107.2 

112.4118.4  125.0 

96.9 

99.9 

103.5 

107.6 

112.3 

117.5 

6            103.1'108.9 

115.7 

123.6|  100.3104.8110.2116.4 

123.4 

8 

107.5  115.2 

124.3 

i 

103.8109.8116.9  125.2 

19 

16 

4 

111.2  115.0 

119.6 

124.8  130.8  137.4 

..  112.3  115.9  120.0 

124.7  129.9 

6            115^5  121.3  128.1 

136.0  144.9  112.7117.2  122.  6!  128.  8 

135.8  143.6 

8           1119.9127.6 

136.7 



116.2  122.2  329.3  137.6 

20 

17 

4             124.4128.2 

132.8 

138.0144.0150.6 

.  .  125.5  129.1  133.2 

137.  9:  143.1 

6         ,  128.7  134.5 

141.3 

149.2158.1 

;  125.  9130.  4135.  8142.0 

149.0156.8 

i 

8            133.1 

140.8 

149.9 

160.4 

• 

129.4135.4 

142.5  150.8 

160.1 

• 

1 

21 

18 

4          ' 

142.2 

146.8 

152.0  158.0 

164,61  139.5 

143.1  149.2 

151.9  157.1 

6             142.7148.5 
8             147.  1  154.8 

155.3  163.2 
163  9  174  4 

172.1 

182.1  1139.  9|144.  4 
J143  4  14Q  4. 

149.8 
156.5 

156.0163.0170.8 
1fU    S  174    1 

22                   19 

4             157.0 

161.6 

166.8172.8 

.  .     J.40.4 

179.  41  . 

157.9  162.0 

166.7 

171.9 

6             157.5163.3 
8            161.9169.6 

170.1 

178.7 

178.0  186.9  196.9    154.7  159.2  164.6:170.8  177.8  185.6 
189.2201.1  (158.2164.2171.3179.6188.9199.4 

23                   20 

4             172.6177.2182.4188.4  195.0 

173.5  177.6 

182.3 

187.5 

6            173.1178.9185.7193.6202.5212.5 

..174.8180.2186.4 

193.4201.2 

8            177  5  185  2  194  3  9n4  s  21  fi  7               17^  fi  17Q  8  1Rfi  Q  10.1  9 

9fU    A  91.1    H 

24                   21 

4          |l  189.0  193.6 

198.8204.8 

211.4'  . 

.  .  189.9  194.0198.7203.9 

6 

189.5  195.3  202.1  210.0218.9  228.9    191  .2196  .6  202  .8 

209.8217.6 

1 

8 

193.9  201.6210.7 

221.2233.1246.4 

190.2196.2203.3211.6 

220.9  231.4 

25                   22 

4 

210.8 

216.0222.0228.6 

.  .  211.2215.91221.1 

6- 

'.  '.  212.5  219.3I227.2  236.1  246.1 

208.4,213.8220.0 

227.0234.8 

1 

8 

211.1218.8227.9238.4 

250.3263.6 

207.4  213.4,220.5228.8238.1  248.6 

26                   23 

4 

.  .  228  .  8 

234.0 

240.0246.6 

229.2 

233.9 

239.1 

6 

'.'.'.'.'.  230.5237.3245.2 

254.1 

264.1 

226.4231.8238.0 

245.0i  252.  8 

8 

229.1  236.8245.9  256.4 

268.3 

281.6 

231.4238.5246.8 

256.1 

266.6 

27                  24 

4             1  247.6 

252.8 

258.  8  265.  4! 

l248.0!252.7 

257.9 

6          !|  249.3  256.1  264.0 

272.9282.9 

250.6256.8263.8 

271.6 

8            247.9255.6,264.7 

275.2 

287.1  300.4 

'.'.  '.'.  '.  250.2257.3265.6274.9 

285.4 

28                   25 

4 

272.4 

278.4 

285.0 

267.6272.3 

277.5 

6             

268  '.9  275.  7 

283.6 

292.5302.5 

.  .  270.2276.4 

283.4 

291.2 

8            267.5 

275.2284.3 

294.8 

306.7320.0 

269.8276.9285.2,294.5 

305.0 

29 

26 

4 

292.8 

298.8305.4 

292.7 

297.9 

6 

8 

289.3296.1  304.0 
295.6304.7315.2 

312.9 
327.1 

322.9 
340.4 

'.'.  '.'.  ^290.2 

290^6296.8303.8 
297.3305.6,314.9 

311.6 
325.4 

30 

27 

4 

292.8 

298.8 

305.4 

292.7 

297.9 

6 

296  '.i 

304.0 

312.9 

322.9 

296.8 

303.8'311.6 

!             8 

'.....  295.6304.7 

315.2 

327.1  340.4 

'.'.'.'.'.   297.3  305.6|314.9|325.4 

100 


TABLE  29 

K 

J             COLUMNS 

SQUARE 
SAFE  LOAD  IN 
CHICAGO  BUILD 

Ma. 

V 

"* 

CORED  COLUMNS 
THOUSANDS  OF  POUNDS 
ING  CODE  REQUIREMENTS 

Af[l  +  (n—  l)p]                               2400-lb.  concrete 
/length\      19                              1:4%  mixture 

ic;    «•'  *    •*>  J    •?•  *  • 

-lilt 

*'\  side  ) 

/*  —  JL6 

fc=480 

Size               Size 
of                  of 
column            core 
(inches)         (inches) 

Number 
of 
rods 

Square  rods                                                   Round  rods 

H 

% 

K 

1     i    1,4 

IK  i!    *A 

1 

1 

IK 

IK 

12                     9 
13                   10 
14                   11 

15                   12 
16                  13 
17                  14 
18                  15 
19                  16 
20                  17 
21                   18 
22                   19 
23                   20 
24                   21 
25                  22 
26                  23 
27                  24 
28                 25 
29                  26 
30                  27 

4 

4 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

I 

I 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

4 

6 
8 

4 
6 

8 

A 

6 
8 

4 
6 

8 

4 

6 
8 

47.1 
56.3 

66.3 
70.5 
74.6 

77.4 
81.5 
85.6 

89.4 
93.5 
97.6 

102.3 
108.5 
110.6 

116.3 
120.4 
124.5 

131.1 
135.3 
139.4 

147.0 
151.1 
155.2 

50.8 
59.9 

69.0 
75.9 

74.3 

45.4 
54.5 

64.6 
67.8 
71.0 

75.6 
78.8 
82.1 

87.6 
90.8 
94.1 

100.6 
103.8 
107.0 

114.5 
117.7 
121.0 

132.6 
135.8 

l48'.4 
151.7 

48.2 
57.3 

67.4 
72.1 
76.7 

78.5 
83.1 
87.8 

90.5 
95.1 
99.8 
103.4 
108.1 
112.7 
117.3 
122.0 
126.7 
132.2 
136.9 
141.5 

148.1 
152.7 
157.4 

164.9 

51.1 
60.7 

70.8 
77.1 

81.8 
88.2 

93.8 
100.2 
106  5 

106.8 
113.-1 
119.5 

120.7 
127.1 
133.4 

135.6 
141.9 
148.3 
151.4 
157.8 
164.1 

168.2 

74.7 
85.7 

97.7 
106.0 

110.7 
119.0 

124.6 
132.9 
141.2 

139.5 
147.8 
156.1 

155.3 
163.6 
171.9 
172.1 

90.1 
102.1 
115.1 

129.0 
139.5 

143.9 
154.4 

159.7 
170.2 
180.7 
176.5 

107.0 
120.0 
133.9 

148.8 
161.8 

164.6 
177.6 

181.4 



81.0 
86.9 

85.3 

90.2 

93.0 
98.9 
104.9 

106.0 
111.9 
117.8 

119.9 
125.8 
131.8 

134.8 
140.7 
146.6 

150.6 
156.5 
162.5 

167.4 

97.3 
105.4 

102.2 

107.9  

110.3 
118.3 

115.2 

120.8 

124.2  129.1 
132.3139.7 
140.3!  

139.1  144.0 
147.1  154.6 
155.2  

154.9159.8 
163.0170.4 
171.1  181.0 
171.7176.6 

134.7  141.0 

149.6 
163.0 

165.5 

178.8 

182.3 

155.9 
171.7 
188.5 

167.9 
172.0 

173.3  179.8  187.2 
179.3  187.9197.8 

185  2  189  5  194  4 

195.6 
200.0 

205.0 
206.3 

165.2 
168.5 

169.5 
174.2 

174.6 
180.9 

186.0 
192.3 
198.7 

204.7 
211.1 
217.4 

224.4 

180.4 
188.7 

189.9 
198.2 
206.5 

208.6 
216.9 
225.2 

228.3 
236.6 
244.9 

248.9 
257.2 
265.5 
270.5 

278.8 
287.1 

283.1 
301.4 
309.7 

316.6 
324.9 
333.2 

349.4 
357.7 

187.0|194.4 
197.5 

194.3  199.2 
204.8212.2 
215.3225.1 

213.0217.9 
223.5230.9 
234.0243.8 

232.7237.6 
243.21250.6 
253.7263.5 

253.3258.2 
263.81271.2 
274.3284.2 

274.9278.8 
285.4292.8 
295.9305.8 

297.5302.4 
308.0315.4 
318.5328.3 

321.0325.9 
331.5338.9 
342.0351.8 

345.5350.4 
356.0363.4 
366.5^76.3 

370.9375.8 
381.4388.8 
391.9401.8 

185.7 
189.8 

204  '.4 
208.5 

191.1  197.5205.0 
197.0205.6215.5 

203.9208.2'213.1 
209.8:216.3223.7 
215.8224.3234.2 

223.6227.9'232.8 

213.4 
226.7 

218.7 
232.1 
245.5 

238.4 

222.8 

225.0 
241.5 

244.7 

183.0 
186.2 

205  '.6 

187.3 
191.9 

206  '.6 
210.7 

224.1 
228.2 

248  '.8 

229.5 
235.4 

250  '.i 
256.1 

235.9 
244.0 

248.5 
256.6 
264.7 

270.1 
278.2 
286.3 

292.7 
300.7 
308.8 

324  '.3 
332.3 

348  '.7 
356.8 

243.4 
253.9 

253.4 
264.0 
274.6 

275.0 
285.6 
296.2 

297.6 
308.2 
318.7 

321.1 
331.7 
342.2 

345.6 
356.2 
366.7 

371.0 
381.6 
392.2 

251.8 
265.1 

259.1 
272.4 
285.8 

280.7 
294.0 
307.4 

303.2 
316.6 
329.9 

326.7 
340.1 
353.5 

351.2 
364.6 
377.9 

376.7 
390.0 
403.4 

261.2 

277.7 

265.3 
281.8 
298.3 

286.9 
303.4 
319.9 
309.5 
326.0 
342.5 

333.0 
349.5 
366.0 

357.5 
374.0 
390.5 

382.9 
399.4 
415.9 

224  .  6 
245  '.3 

225.7 
230.3 

246  '.3 
251.0 

230.7 
237.1 

25i'.4 
257.7 

271.7 
277.7 

267.9 
272.6 

273.0 
279.3 

270.4 

293.6 

3ie>'.5 

294.3 
300.2 

3i7'.8 
323.8 

342  '.3 
348.2 

295.5 
301.9 

sig'.i 

325.4 

343.5 
349.9 

295.1 

sis  '.7 

..... 

343.1 

374.2 
'373.7382.3 



374.8 
375.3(383.1 

101 


COLUMNS 


TABLE  30 


UVH 

1  J 

SQUARE 
LOAD  IN 
JO  BUILD 

Ma 

CORED  COL1 
THOUSANDS 
ING  CODE  RI 

Afc[l  +  (n-l)p 
/length} 

JMNS 

OF  POUNDS 
SQUIREMENTS 

] 
2 

-  Column  $fre  > 

SAFE 
CHICAC 

2900-  Ib.  concrete 
1:3  mixture 

n          1  ft 

1 
1 

71  —  J.U 

fc  =  580 

*'  V  side   )  ~ 

JJ3SSS 

Size 
of 
column 
(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

X|« 

% 

1 

m 

IK 

H 

X 

H 

i 

.«  |  .« 

12 
13 
14 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

9 
10 
11 

12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 

4 
4 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 

6 

8 

4 
6 
8 

55.1 
66.2 

78.3 
82.4 
86.5 

91.7 
95.7 
99.8 

106.2 
110.2 
114.3 

121.8 
125.9 
130.0 
138.7 
142.7 
146.8 

156.6 
!l60.7 
164.8 

175.8 
179.8 
183.9 

266  '.i 

204.2 

22i.6 
225  7 

58.7 
69.8 

81.9 
87.8 





53.4 
64.4 

76.6 
79.8 
83.0 

89.9 
93.1 
96.3 

104.4 
107.6 
110.8 

120.1 
123.3 
126.5 

136.9 
140.1 
143.3 

iss'.i 

161.3 

177  '.2 

180.4 

i97.5 
200.7 

219  .0 
222  2 

56.2 
67.2 

79.4 
84.0 
88.6 

92.8 
97.4 
102.0 

107.3 
111.9 
116.5 

122.9 
127.5 
132.1 

139.7 
144.3 
149.0 

157.7 
162.3 
166.9 

176.9 
181.5 
186.1 

197.2 
201.8 
206.4 

223  '.2 
227  8 

59.5 
70.6 

82.7 
89.0 

96.1 
102.4 

110.6 
116.9 
123.1 

126.2 
132.5 
138.8 

143.1 
149.3 
155.6 

161.0 
167.3 
173.6 

180.2 
186.5 
192.7 

200.5 
206.8 
213.0 

221.9 
228.2 
234  5 

86.6 
99.9 

114.4 
122.6 

130.1 
138.3 

146.9 
155.1 
163.3 

164.9 
173.1 
181.3 

184.0 
192.2 
200.4 

204.3 
212.5 
220.7 

225.8 
234.0 
242.2 

104.3 
118.8 
134.4 

151.3 
161.6 

169.2 
179.6 

188.4 
198.8 
209.2 

208.7 
219.1 
229.5 

230.1 
240.5 
251.0 

123.6 
139.3 
156  .  1 

174.1 
186.9 

193.2 
206.1 

213.5 
226.4 

235.0 

247.8 
260  .  fi 

86.2 

95.3 
101.1 

109.8 
115.6 
121.5 

125.4 
131.3 
137  2 

99.5 

104.4 

114.0 
122.0 

118.9 

124.5 



129.7 
137.7 

134.6 

140.1 

142.3 
148.1 
154.0 
160.2 
166.1 
172.0 

179.4 
185.2 
191.1 

199.7 
205.5 
211.4 

221.1 
227.0 
232.9 

146'5 
154.5 
162  5 

151.4 

161.8 

156.9 

163.1 

164.5 
172.5 
180.5 

183.6 
191.6 
199.6 

203.9 
211.9 
219.9 

225.4 
233.4 
241.4 

169.4 
179.8 

188.5 
198.9 
209.4 

208.8 
219.2 
229.7 

230.3 
240.7 
251.1 

174.9 
188.1 

181.1 

194.1 
207.3 

214.4 
227.6 

235.8 
249.0 
262.2 

200.3 

220.6 
236.9 

242.0 
258.3 

243.8 
249.6 
255.5 

267.5 
273.4 
279.3 

248.0 
256.0 
264.0 

271.8 
279.8 
287.8 

296.7 
304.7 
312.7 

322.8 
330.8 
337.9 

350.1 
358.1 
366.1 

252.9 
263.3 
273.8 

276.7 
287.1 
297.5 

301.6 
312.0 
322.5 

327.7 
338.1 
348.6 

355.0 
365.4 
375.8 
383.4 
393.8 
404.3 

413.0 
423.4 
433.8 

443.7 
454.1 
464.6 

258.4 
271.6 
284.9 

282.2 
295.4 
308.6 

307.2 
320.4 
333.6 

333.3 
346.5 
359.7 
360.5 
373.7 
386.9 

388.9 
402.1 
415.4 

418.5 
431.7 
444.9 

449.3 
462.5 
475.7 

264.6 
280.9 

288.4 
304.7; 
321.0| 

313.4 
329.7 
346.0! 

339.5 
355.9 
372.1 

366.7 
383.0! 
399.3 

395.1 
411.4 

427.8, 

424.71 
441.0 
457.3; 

455.5 

471.8 
488.1 

245  '.8 
250.5 

244.6 
250.8 
257.1 

268.3 
274.6 
280.9 

248.4 
256.6 
264.8 

272.2 
280.4 
288.6 

297.1 
305  .  3 
313.5 

323.2 
331.4 
339.6 

350.5 
358.7 
366.9 

378.9 
387.1 
395.3 

4i6'.7 
424.9 

252.8!257.6 
263.1  270.4 
273.6,283.3 

276.5281.4 
286.9294.2 
297.4307.0 

301.5  306.3 
311.9319.2 
322.3  332.0 

327.6332.4 
338.0345.3 
348.4358.1 

354.8359.7 
365.2372.5 
375.7385.3 

383.3388.1 
393.6400.9 
404.1  413.8 

412.8417.7 
423  .  2  430  .  5 
433.7|443.3 

443.8448.4 
454.0461.3 
464.4474.1 

244.2 
248.3 

268  !  6 
272.1 

244.8 

268  '.6 
293  .  5 

269.6 
274.2 

298.3 
304.2 

294.6 
299.2 

299.6 
305.8 

325  '.7 
831.9 

352  '.9 
359.2 

38i'.3 
387.6 

4i6.9 
417.2 

297.0 

323  '.i 

324.4 
330.3 

320.7 
325.3 

351.7 
357.6 

350.4 

352.5 

378  '.8 

380.1 
386.0 

409  '.7 
415.6 

386.5 
393.5 

iie'.i 

424.1 

38i.6 

iiois 

446  '.3 

446.8 
454.8 

447.4 
455.6 

447.9 

102 


TABLE  31 
(  Column  sire    J 

SQUARE  CORED  COLUMNS 

COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
.OS  ANGELES  BUILDING  CODE  REQUIREMENTS 

1:6  mixture 

P  =  Afc(l  +  (n-l)p}                               n=15 
fc=550 

j:    e'  •»'.'.  -a-  "• 

BVJ 

<:$£* 

mm 

-  i^-SliXs. 

3M 
Jj'l 

l     J 

Size 
of 
column 
(inches) 

Size 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

X 

H 

1 

1H 

IK 

H 

H 

K 

1 

1M 

IK 

12 
13 

14 
15 
16         * 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 

29 
30 

9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

26 
27 

4 
4 
6 
8 
4 
6 
8 
4 
6 
8 
4 
6 
8 
4 
6 
8 
4 
6 
8 

6 

8 

4 
6 
8 

4 
6 

8 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 

8 

4 
6 
8 

4 
6 
8 

4 
6 
8 

6 

8 

6 

8 

56.6 
67.0 
73.0 
79.0 
78.6 
84.5 
90.6 
91.2 
97.2 
103.2 

111.0 
117.0 

125.8 
131.8 

141.8 
147.8 

61.9 
72.3 
81.0 
89.7 
83.9 
92.6 
101.2 
96.5 
105.2 
113.9 
110.3 
119.0 
127.6 
125.1 
133.8 
142.5 
141.1 
149.8 
158.4 

iee'.s 

175.5 

iss'.o 

193.6 

204  '.2 
212.9 

233.2 
254  '.7 

68.1 
78.6 

75.4 
85.8 

54.0 
64'.  5 
69.2 
73.9 
76.0 
80.7 
85.4 

93.4 
98.1 

107.1 
111.8 

58.2 
68.6 
75.4 
82.2 
80.2 
87.0 
93.7 
92.8 
99.6 
106.4 
106.6 
113.4 
120.1 

63.1 
73.5 
82.8 
I  92.0 
85.1 
94.3 
103.6 
97.8 
107.0 
116.2 
111.5 
120.7 
130.0 
126.4 
135.6 
144.8 
142.3 
151.5 
160.8 

68.7 
79.2 

|  75.2 
85.6 

92.8 

J  90.3 

J  91.3 

90.7 
102.8 

103.4 
116.5 

97.2 

104.4 

90.1 
101.9 

97.4 

105.5 

112.8 

112.4 
109.8 

117.0 

102.8 
114.5 
Il26.3 
116.5 
128.3 
140.1 
131.4 
143.1 
154.9 
147.3 
159.1 
170.9 

164.4 
176.1 
187.9 

182.5 
194.3 
206.1 

2i3'.5 
225.3 

233.9 
245.7 

255.3 
267.1 

110.0 

118.2 

127.3 

J125.4 

125.1 

130.8 
J149.6 

145.6 
164.5 

1127.6 
117.1 
129.2 
141.3 
132.0 
144.1 
156.2 
147.9 
160.0 
172.1 

165.0 
177.1 
189.2 

183.1 
195.2 
207.3 

2i4'.5 
226.6 

234  '.8 
246.9 

256  '.3 

268.4 

123.6 

138.8 
J154.2 
138.4 
153.7 

123.8 
139.2 
|154.6 
138.6 
154.0 

131.9 

141.1 

151.4 

146.8 
166.2 

155.9 
180.0 

126.7 

128.2 
135.0 

169.4 
154.6 
170.0 
185.4 

171.6 
187.0 
202.4 

189.8 
205.2 
220.6 

209.0 
224.4 
239.8 
229.4 
244.8 
260.2 

250.8 
266.2 
281.6 

|169.0  183.4 
154.4161.6 
169.6180.4 
185.0|199.4 

171.4  178.6 
186.7197.5 
202.0216.4 

189.6196.8 
204.8215.6 
220.2234.6 

208.8!216.0 
224.1  234.8 
239.4253.8 

229.2'236.4 
244.4255.2 
259.8274.2 

250.6257.8 
265.9276.7 
281.2295.6 
.  .280.4 

162.7 
182.2 
201.7 

179.8 
199.2 
218.7 

197.9 
217.4 
236.9 

217.2 
236.6 
256.1 

237.5 
257.0 
276.5 

259.0 
278.5 
297.9 

281.5 
301.0 
320.5 

305  2 

171.9 
196.0 

142.6 

144.2 
150.9 

188.9 
213.0 
237.1 

207.1 
231.2 
255.2 

226.3 
250.4 
274.5 

246.7 
270.8 
294.8 

268.1 
292.2 
316.3 

290.7 
314.8 
338.8 

314  3 



161.2 
168.0 

168.6 
177.8 

i86'.7 
196.0 

206.6 
215.2 

226  '.3 
235.6 

257  '.6 

164.8 

iss'.o 

186.1 
205  '.4 

::::: 





••'•• 



277  '.2 

277.9 
289.7 

288.8 
304.2 



279  '.6 

278.8 
290.9 

288.4 
303.8 

299.2 
318.2 

304.0 
322.9 
341.8 

347.6 
366.5 

373.4 
392.4 

400.4 
419.4 

428.5 
447.4 

457.6 
476.6 

312.4 
327.8 

324  .  6 
344.1 

338.4 
362.5 

339.1 
363.2 
387.2 

364.9 
389.0 
413.1 

391.9 
416.0 
440.0 

444.0 
4fi8   1 

312.1 
327.4 

336.8 
352.2 

362.7 
378.0 

405.0 

313.3 

3i4.6 

337.2 
352.6 

349.4 
368.9 



338.1 

•  •  •  •  • 

:.... 



339.3 
365  '.2 
392.1 

.'.'.'.'. 



363  '.9 

363.0 
378.4 

375.2 
394.7 

402.2 
421.7 

430.2 
449  7 



..... 

..... 

405.4 

433  4 

433.0 

459.4473.2 
478.9,497.2 

462.6 

462.  2j 

Below  and  to  right  of  zig-zag  lines,  reinforcement  is  more  than  4  per  cent. 

103 


COLUMNS 


TABLE  32 


ROUND  CORED  HOOPED  COLUMNS 


Column  size 


2000  -Ib. 
1:6  mixti 

nje 

JOINT  C01V 

concrete        Volume  of 
Max. 

1MITTEE  RECOMMENI 

P  =  Afc(l  +  (n-l}p] 
Hooping  =  1%  of  Volume 
/unsupported  length\ 

)ATIONS 

of  Core 
10 

©1 

f     7nn 

\      core  diameter      / 

t^&r 

Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

14 

1 

1H       1>4 

H 

H 

7A 

l 

1H 

1M 

12 
13 

14 
15 

16 
17 

18 

19 
20 
21    . 
22 
23 

24 
25 

8 
9 

10 
11 

12 
13 
14 

15 

16 
17 
18 
19 

20 
21 

6 

6 

8 

6 

8 

6 
8 
10 

6 
8 
10 

6 
8 
10 

6 
8 
10 
12 

'        6 
8 
10 
12 

8 
10 
12 
14 

8 
10 
12 
14 

8 
10 
12 
14 

8 
10 
12 
14 
16 

8 
10 
12 
14 
16 

10 
12 
14 
16 

53.2 

62.5 
68.6 

73.0 
79.1 

84.5 
90.6 
96.6 

97.2 
103.3 
109.3 

110.9 
116.9 
123.0 

125.7 
131.8 
137.8 
143.8 

141.7 

147.8 
153.8 
159  .8 

164.9 
170.9 
176.9 
182.9 

183.0 
189.0 
195.0 
201.0 

208  '.3 
214.3 
220.3 

81.0 

92.5 
101.1 

105.2 
113.8 
122.5 

118.9 
127.5 
136.2 

133.7 
142.3 
151.0 
159.7 

149.7 
158.3 
167.0 
175.7 

175.4 
184.1 
192.8 
201.4 

193.5 
202.2 
210.9 
219.5 

212.8 
221.5 
230.2 
238.8 

233.1 

241.8 
250.5 
259  .  1 
267.8 

254.5 
263.2 
271.9 
280.5 
289.2 

285.8 
294.5 
303.1 
311.8 

101.9 
114.6 

128.3 
140.0 

143.1 
154.8 
166.6 

159.1 
170.8 
182.6 

187.9 
199.7 
211.5 

206.0 
217.8 
229.6 
241.4 

225.3 
237.1 
248.9 
260:7 

245.6 
257.4 
269.2 
281.0 
292.8 

267.0 
278.8 
290.6 
302.4 
314.2 

301.4 
313.2 
325.0 
336.8 

139.1 
153.9 

169.9 
185.3 

202.4 
217.8 

220.5 
235.9 

239.8 
255.2 
270.6 

260.1 
275.5 
290.9 
306.3 

281.5 
296.9 
312.3 
327.7 
343.1 

319.5 
334.9 
350  .  3 
365.7 

166.1 

182.1 
218.7 
236.8 

256.1 
275.6 

276.4 
295.9 

297.8 
317.3 
336.8 

339.9 
359.4 

. 

274.4 
294.7 

316.1 
340  .  1 

362.7 

67.5 

78.0 
85.6 

89.5 
97.1 

102.2 
109.8 
117.5 

115.9 
123.5 
131.2 

130,7 
138.3 
146.0 
153.6 

146.7 
154.3 
162.0 
169.6 

171.4 
179.1 
186.7 
19r?4 

189.5 
197.2 
204.8 
212.5 

208.8 
216.5 
224.1 
231.8 

229.1 
236.8 
244.4 
252  .  1 
259.8 

250.5 
258.2 
265.8 
273.5 
281.2 

280.8 
288.4 
296.1 
303.8 

99.6 

112.3 
123.3 

126.0 
137.0 

137.9 

140.8 
151.8 
162.8 

156.8 
167,8 
178.8 
189.9 

184.9 
195.9 
206.9 

2ig":o 

203.0 
214.0 
225.0 
236  1 

152.7 
167.7 

166.5  

168.7 
183.7 

182.5 

.  .  f>  

: 

200.8 
215.8 

219.2 

218.9 

23L-9 

237.3 

• 

222.3 
233.3 
244.4 
255.4 

- 

242.6 
253.6 
264.7 
275.7 
286.7 

264.0 
275.0 
286.1 
297.1 
308.1 

297.6 
308.7 
319.7 
330.7 

238.2 
253.2 
268.2 

256.6 
276.2 

277.4  

258.5 
273.5 
288.5 
303.5 

m 

309.9 
32T.9 
339.9 

317.5 
332.5 
347.5 
362.5 

276.9 
296.5 

298.3 
317.9 
337.5 

340.5 
360  .  1 

297  7 

319.1  342.4 
343.9  ... 

366  .  5  



j  

228.6 
234.6 
240.6 
246.6 

256  '.6 
262.0 
268.0 

278  '.6 
284.6 
290.6 

104 


TA^LE  32 


Column  Size     ^ 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Volume  of  Hooping  =  1%  of  Volume  of  Core 

,_       /unsupported  length\ 
Max.  I  —j-. —  I  =  10 

\       core  diameter      / 


COLUMNS 


2000- Ib.  concrete 
1:6  mixture 

71=15 

fc=700 


Size  I  Diameter 
of                   of 

column  i        core 

(inches)  I  (inches) 


Number 

of 
rods 


Square  rods 


Round  rods 


?s 


L>7 


28 


29 


SO 


lio 


27 


20 


10 
12 
14 
16 
18 

10 
12 
14 
16 
18 

10 
12 
14 
16 
18 

10 
12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 
24 


304.4 .321.21341.1  364.1  390.1 
312.0332  3!356  1  383.7414.9 
319.7  343. 31 371.1  403? 
327.4354.3 
335.0365.3 


346.0 
357.1 
368.1 
379.1 
390.1 


365.9388.9414 

380.91408.5439 

395.9J428.1 

410.9447.7 

425.9 


1309.4325.0343 

J318.1  336.8 

308.2  326.7  348.6 
314.2335.4360.4 
320.2  344.0  372.2 


444.0 


469.8 


371.8391.7414.7440.7 
382. 9  406. 7  434. 31465. 5 
393.9  421.7  453.9:490.3 

404. 91436.71473. 5; 

315. 9!451. 7J493.1  .. 


398.7:418.6441.6476.6496.7! 

409.8  433.6  461 .2!492.4!527. 4 

420.81448.6480.8517.2 

431.8463.6500.4 

442.8478.6520.0 

453.9493.7 


437.8461.6489.2520.4 
448.8  476.6508.81545.2 
459.8491.6528.4  570.0 
470.8  506.6548.0 
481.9521.7:567.6 


467.0490 
478.01505. 
489.0520 

500.0  535 

511.1  550 
522 . 1  565 


.6 

615.2 


8518.4549.6584 

8538.0574.4 

8557.6599.2 

8]577.2  624.1 

9596.8 

9616.4 


| 

.  497.3521 
.  508.3536 
,  519.3551 
.  530.3566 
.  541.4581 
.  552.4596.2646.7  .. 


555.4 


1548.7579.9614.9 
1  568.3  604.7645.5 
1  587.9:629.5  ...... 

1  607.5654.4 
2627.1 


,  528.6552.4580.0611.2646.2 
.539.6567.4599.6636.0676.8 
.  550.6582.4619.2660.8707.4 
.  561 .6  597.4  638.8  685. 7J |, 

572. 7  612.5|658. 4'710. 5i j, 

583.7627.5678.0'.. 


...  584.8:612.4:643.6678.6 

572.0  599.81632.0  668.4  709.2 
583.0614.8651.6|693.2  739.8 
594. 0629. 8^671. 2718.1  770 .4 

605.1  644.9690.8742.9 
616.1  659.9710.4  767.7 
627.1  674.9730.0,... 


349.8367.9388.3411.1 
8435.2 


334.2 
342.9  361 
351.5373. 
360.2  385.2  414 
368.8397.0429.4 


375.6 
.7387.4 


393.7414 
409.1 

3399.2424.5 
0439.9 
.2 


368 
377. 

386.0411 
394.6422 


402.5420.6 
6414.3436.0 


.11363.5386.3 
358.5  383.01410.4 
373.9402.5 
389.3 
404.6 


383.3 
398.7 


407. 

427.3 

446.8 


8455. 


395. 

404.2426.1 
412.9  437.9466 
421.5449 
430.2461.5497 


423.6442.3464 

432.2454 

440.9465.9494 

449.5477 

458.2489.5525 


.0 
479.4 

.8 
510.1 

.5 


471.5493.2517.754 

483.3 

495.1 


461.4 

470.1 

478.7506.9539 

487.4518 

496.1 


.7 
530.4 


508.6 
524.0  556 

.3 

554.7595 
570.1 


501 
491.7513 
500.4  525 
509.0537 
517.7549 
526.4560 

544 

531.7556 
540.3568 
549.0580 
557.7592 


'564.1 


.8523, 
.6538, 
.4'554 
.2569 
.0585 
.7600 

.1;554, 
.9570. 
.7585. 
.5J600, 
.3'616. 
.0631. 


433. 
453.1 
472.6 
492.0 


436.9 
6461.0 
485.0 


441.0463 
460 . 5  487 
451.4  480.0 

499.5  536 
518.9 


488. 

508.0539 

527.5 

546.9 

566.4 


537.2 
.7 

576.1 
.6 

615.1 


5548. 
9|567. 
3587. 
6606. 
0625. 
4645. 

8579. 
2,598. 
61618. 
9,637. 
3  657. 
7676. 


.s 
.9 

511.9 
.0 


5  51; 


.9 
564.0 


5.1 
569.1 
593.2 
617.2 


0575.4 
5599.4 
0  623 . 5 
4647.5 
9671.6 
4 1 

3  606.7 
8  630'.  7 
3  654.8 
7678.8 
2  702.9 
7 


565.51587.2  611.7  639.1 
577.3602.6631.2663.1 
589.1  618.0650.7687.2 


1572.7600.9633.3670.1  711.2 
581 .4  612.7  648.7  689.6  735.3 
590.1  624.4  664.1  709.1  759.3 
598.7636.2!679.5;728.6 


105 


COLUMNS 


TABLE  32 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Column  size  ._.> 


2000 -lb.  concrete 
1:6  mixture 
n  =  15 
fc=700 


l}p] 
Volume  of  Hooping  =1%  of  Volume  of  Core 


Max 


unsuPP°rted 

core  diameter       / 


Size 
of 

column 
(inches) 


3f> 


36 


37 


38 


Diameter 

of 
core 

(inches) 


10 


31 


32 


33 


34 


35 


3(1 


37 


38 


Number 

of 
rods 


Hi 
18 
20 
22 
24 
26 
28 

Hi 
18 
20 
22 
21 
26 
28 

Hi 
18 
20 
22 
21 
26 

28 

30 


Square  rods 


1605.6  633. 4,665. 6i702.0  742.8 
616.6  648.4)685.2  726.8  773.4 


.627.6663.4 


704. 8  751. 71804.0 


638  7678.5  724.4  776.5 
.649.7693.5744.0801.3 
.660.7708.5763.6' 


667.9700, 
682.9719, 
697.9  739, 
713.0758 

728.01778, 
743.01798, 


703.7i735. 

718.7755. 

733.7  775. 
748.8794. 

763.8!814. 

778.8:833. 
>793.8'853. 

740.5772. 
i  755.5|  792. 

770.5811. 
1785.61831. 
'800.6:851. 

815.6870. 

830.6890. 

778.5810. 

793.5J830. 

808.5849. 

823.6;869. 
. '838.6'889. 

853.6908. 
.  I868.6J928. 

,832.5869, 
'847. 5(888, 

862.6;908 
i877.6i928 
I892.6J947 
;907. 61967 

922.61986 


1  736 

7  761 
3786 
9811 
5835 
1  860 

9772 
5,797 
11822 
7!846 
3  871 
9  896 
5  921 


5777.3 
3807.9 
2838.5 
0869.2 


3813.1 
1  843 . 7 
0874.3 
8905.0 


7  809.11849.9 
3833.9880.5 
9i858. 8)911.1 
51883.6)941.8 
1:908.4)972.4 
71933.2  ..... 
3  958.0). 

7847.1887.9 
3  871.9918.5 
9  896.8,949.1 
5  921.6979.8 
1  946.4 
7971.2 
3  996.0 


3  910.91957.5 
,9  935.8)988.1 


1010 
1041 


5  960.6 
1  985.4 
71  1010 
3)  1035 
9  1060 


872.6909.4  951.0997.6 


887.6929.0975.9 


902.7  948.6 
'917.7'968.2 
^932.7987.8 
1947.7  1007 
!962.7  1027 


1001 
1025 
1050 
1075 
1100 


1019 
1049 
1080 
1111 


913.9950.7992.3 
928. 9970. 3'  10171 
1944.0  989.9)  1042) 
959.0)  1009  1067 
974.0  1029  1092 


989.0 
1004 
1019 


1049  1116 


1068 
1088 


1141 
1166 


1028 
1059 
1089 
1120 
1151 


1039 
1069 
1100 
1131 
1161 
1192 
1223 


Round  rods 


606. 
615. 
623. 
632. 


610.9636.2  664.8696.7 
622.7651.6684.3  720.8 
3  634.5  666.9  703.7|744.8 
0646.3682.3723.21768.9 
7658.0697.7742.7792.9 
3669.8713.1  762.2  817.0 


645. 
657.2  686 


680.8 

692. 

704 


4670.7699.3  731.2 
718.8755.3 
0701.4  738.2  779.3 
716.8757.7J803.4 
5732.2  777.2827.4 
.3747.6796.7851.5 


753.4 
765.1 


693.0 

704.8737.2 

716.6752 

728.3 

740.1 

751.9 


706.5735.1  767.0 
721.9  754.6791.1 


774.0815.1 

.6  793.5)839.2 
768.0:813.0863.2 
783.4  832.5:887.3 
798.8,852.0911.3 


743.3j771.9803.8 
729.8758.7  791. 4;827. 9 
741.6774.0)810.8:851.9 


789.4l830.31876.0 
804.81849.8)900.0 


776. 9  820. 2'869. 31924.1 
788.7835.6!888.8948.1 


781.3  809.9  841.8 
767.8)796.7i829.4865.9 
779.6812.0848.8i889.9 
791.4)827.4,868.3  914.0 
803.1  842.8:887.8938.0 
814.9)858.2  907.3  962.1 
826.7873.6926.8,986.1 


835.7868.4;904.9 
818.6851.0.887.8928.9 
830.4866.4  907.3953.0 
842.1(881.8926.8977.0 


853.9  897.2  946.3 
865.7912.6965.8 

877.51928.0985.3 


1001 
1025 
1049 


875.8908.5945.0 
858.71891.1  927.9969.0 
870.5906.5947.4993.1 
882.2921.9966.9  " 
894.0937.3986.4 


905.8952.2 
917.6968.1 


1006 
1025 


1017 
1041 
1065 
1089 


...1917.1949.8986.3 
...1932.4969.2    1010 

911.8I947.8988.7 


923.5963.2 
935.3978.6 
947.11994.0 
958.9  1009 
970.7  1025 


1008 
1028 
1047 
1067 
1086 


1034 
1058 
1083 
1107 
1131 
1155 


100 


TABLE  32 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Volume  of  Hooping 
Max. 


1%  of  Volume  of  Core 

**ngth\  ==w 
\      core  diameter      I 


2000 -Ib.  concrete 
1:6  mixture 
n=15 
fc=700 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

T4  :  l 

i 

IX 

U4 

X 

H 

H 

1 

IX 

IK 

43 
44 

45 
46 
47 
48 
49 
50 

39 
40 

41 
42 
43 
44 
45 
46 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

20 
22 
24 
26 
28 
30 

956.2 
971.2 
986.3 
1001 
1016 
1031 
1046 
1061 

993.0 
1012 
1032 
1052 
1071 
1091 
1111 
1130 

1036 
1056 
1076 
1095 
1115 
1134 
1154 
1174 

1101 
1120 
1140 
1159 
1179 
1199 
1218 

1146 
1166 
1186 
1205 
1225 
1244 
1264 

1193 
1213 
1232 
1252 
1271 
1291 
1311 

1241 
1260 
1280 
1300 
1319 
1339 
1358 

1290 
1309 
1329 
1349 
1368 
1388 
1407 

1359 
1379 
1399 
1418 
1438 
1457 

1035 
,  1060 
1084 
1109 
1134 
1159 
1184 
1208 

1078 
1103 
1128 
1153 
1178 
1202 
1227 
1252 

1148 
1172 
1197 
1222 
1247 
1272 
1296 

1193 
1218 
1243 
1268 
1292 
1317 
1342 

1240 
1265 
1289 
1314 
1339 
1364 
1389 

1288 
1313 
1337 
1362 
1387 
1412 
1437 

1337 
1361 
1386 
1411 
1436 
1461 
1485 

1411 
1436 
1461 
1486 
1511 
1535 

1081 
1112 
1143 
1173 
1204 
1234 
1265 
1296 

1125 
1155 
1186 
1217 
1247 
1278 
1308 
1339 

1200 
1231 
1261 
1292 
1322 
1353 
1384 

1245 
1276 
1307 
1337 
1368 
1399 
1429 

1292 
1323 
1353 
1384 
1415 

ii£ 

1340 
1371 
1401 
1432 
1463 
1493 
1524 

1389 
1420 
1450 
1481 
1511 
1542 
1573 

1470 
1500 
1531 
1561 
1592 
1623 



959.4 
974.7 
990.1 
1005 
1021 
1036 
1052 
1067 

1003 
1018 
1034 
1049 
1064 
1080 
1095 
1110 

1063 
1078 
1094 
1109 
1124 
1140 
1155 

1108 
1124 
1139 
1155 
1170 
1185 
1200 

992.1 
1012 
1031 
1051 
i  1070 
1090 
1109 
;  1128 

1036 
1055 
1074 
1094 
1  1113 
1133 
1152 
1172 

1100 
1119 
1139 
1158 
1178 
1197 
1216 

1145 
1165 
1184 
1204 
1223 
1243 
1262 

1192 
1211 
1231 
1250 
1270 
1289 
1309 

1240 
1259 
1279 
1298 
1318 
1337 
1357 

1289 
1308 
1328 
1347 
1367 
1386 
1406 

1358 
1378 
1397 
1417 
1436 
1456 

1029 
1053 
1077 
1101 
i  1125 
1149 
1173 
1197 

1072 
1096 
1120 
1144 
1168 
1192 
1216 
1240 

1141 
1165 
1189 
1213 
1237 
1261 
1285 

1186 
1210 
1234 
1258 
1282 
1307 
1331 

1233 
1257 
1281 
1305 
1329 
1353 
1377 

1281 
1305 
1329 
1353 
1377 
1401 
1425 

1330 
1354 
1378 
1402 
1426 
1450 
1474 

1404 
1428 
1452 
1476 
1500 
1524 

i  



••••• 

954.1 
965.8 
977.6 
989.4 
1001 
1013 

ioog 

1021 
1033 
1045 
1056 

1654 
1066 
1077 
1089 
1101 

iiii 

1123 
1135 
1147 

1 



P 

1015 
1030 
1045 
1060 
1075 
1090 
1105 

1059 
1074 
1089 
1104 
1119 
1134 
1149 



1  

1 

:  :  :  :  . 

•  •  •  -  - 

1120 
1135 
1150 
1165 
1180 
1195 

iiee 

1181 
1196 
1211 
1226 
1441 

i2i4 
1229 
1244 
1259 
1274 
1289 

i 

1170 
1186 
1201 
1217 
1232 
1247 



1170 
1182 
1193 

::::: 

'1218 
1229 
1241 

1218 
1234 
1249 
1265 
1280 
1295 



1278 
1293 
1308 
1323 
1338 

i328 
1343 
1358 
1373 
1388 

1283 
1298 
1313 
1329 
1344 

'1278 
1290 



1333 
1348 
1363 
1379 
1394 

1328 
1340 

• 

107 


COLUMNS 


TABLE  33 


2500 -Ib.  concrete 
1:4%  mixture 
n=12 
fc=870 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

P=Afe[l+(n-l)p] 

Volume  of  Hooping  —  1%  of  Volume  of  Core 

Max  (unsuPP°rted  length\  =  w 

'  \       core  diameter       I 


fc  Column  size    >i 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

« 

H 

K 

1 

1H 

IK 

1 
% 

K 

K 

1 

IK 

llA 

12 
13 

14 
15 

16 

17 
18 

19 
20 
21 
22 
23 

24 
^ 

25 

8 
9 

10 
11 

12 
13 
14 

15 
16 
17 
18 
19 

20 
21 

6 

6 

8 

6 

8 

6 
8 
10 

6 

8 
10 

6 
8 
10 

6 
8 
10 
12 

6 
8 
10 
12 

8 
10 
12 
14 

iS 

12 
14 

X   8 

10 
12 
14 

ii 

12 
14 
16 

8 
10 
12 
14 
16 

10 
12 
14 
16 

1 

61 

73 

79 

86 
92 

100 
106 
112 

116 
122 
128 

133 
139 
145 

152 
157 
163 
169 

171 
177 
183 
189 

198 
204 
210 
216 

221 
227 
233 
239 

;  -2&i 

257 
263 

"276 

282 
288 
294 

"309 
314 
320 

337 
342 
348 

94 

108 
116 

124 
132 
141 

141 
149 
158 

159 
168 
176 
185 

179 
188 
196 
204 

209 
217 
226 
234 

231 
240 
248 
257 

255 
264 
272 
281 

280 
289 
297 
306 
314 

307 
316 
324 
333 
341 

344 
352 
361 
369 

117 
133 

150 
161 

168 
180 
191 

188 
200 
211 

221 
233 
244 

244 
255 
267 
278 

267 
279 
290 
302 

293 
304 
316 
327 
339 

319 
331 
342 
354 
365 

359 

370 
382 
393 

161 
179 

199 
214 

235 
250 

258 
273 

282 
297 
312 

307 
322 
337 
352 

333 
349 
364 
379 
394 

377 
392 
407 
422 

191 
211 
251 
274 

298 
317 

323 
342 

349 
368 

388 

396 
416 

3ir, 

341 

367 
391 

419 

78 

91 

98 

105 
113 

115 

121 
128 
136 

138 
145 
153 

156 

164 
171 
179 

176 
184 
191 
199 

205 
212 
220 
227 

!  227 
1  235 
1  242 
i  250 

251 
259 
266 
274 

;  277 
i  284 
292 
299 
306 

303 
311 
318 
326 
333 

339 
346 
354 
361 

131 
141 

148 
158 

166 
177 
189 

186 
197 
208 
218 

218 
229 
240 
250 

241 
251 
262 
273 

264 
275 
286 
297 

290 
300 
311 
322 
333 

316 
327 
238 
349 
359 

355 
366 

377 
388 

::::  .... 

159 

178 
193 

198 
212 

234 

248 

191 

211 

252 

256 
271 

280 
295 
309 

305 
320 
335 
349 

332 
347 
361 
376 
391 

375 

389 
404 
419 

274 

298 
317 

323 
342 

350 

369 
388 

;::: 

397 
416 

318 
344 

.... 

370 
394 

422 

108 


TABLE  33 

•^  Columr>  sift?    tt 

ROUND 
SAFE  LOAI 
JOINT  CO1V 

Volume  of 
Max. 

CORED  HOOPED  COLl 
)  IN  THOUSANDS  OF  ] 
IMITTEE  RECOMMENI 

P=Afe(l  +  (n-l)p] 
Hooping  =1%  of  Volume 
/unsupported  length\ 

IMNS 
>OUN 
)ATIC 

of  a 

10 

COLUMNS 

DS 
)NS 

9re 

2500  -lb.  concrete 
1:4]^  mixture 
n  =  12 
fc=870 

•H 

\      core  diameter      / 

Tt*J&r 

Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

% 

H 

1 

IK       \Vi 

H 

H 

7A 

1 

IH 

IH 

26 
27 
28 
29 

30 
31 

32 
33 
34 

22 
23^ 
24 
25 

26 
27 

• 

28 
29 
30 

10 
12 
14 
16 

18 

10 
12 
14 
16 

18 

10 
12 
14 
16 
18 

10 
12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 
24 

368 
376 
383 
391 
398 

385 
395 
406 
417 
428 

415 

426 
437 
448 
458 

447 
458 
469 
480 
490 

481 
492 
502 
513 
524 
535 

526 
537 
548 
559 
570 

563 
574 
584 
595 
606 
617 

600 
611 
622 
633 
643 
654 

639 
650 
661 
672 
682 
693 

404 
419 
433 
448 
463 

435 

449 
464 
479 
493 

467 
482 
496 
511 
525 

500 
515 
530 
544 
559 
574 

550 
564 
579 
594 
608 

586 
601 
615 
630 
645 
659 

624 
638 
653 
668 
682 
697 

663 
677 
692 
707 
721 
736 

703 

718 
732 
747 
762 
776 
791 

426 

452 

373 

381 
390 
398 
407 

404 
412 
421 
429 
438 

'444 
453 
461 
470 

'478 
486 
495 
503 
512 

513 
521 
530 
538 
546 

'557 
566 
574 
583 
594 

'595 
603 
612 
620 
629 

'e>4i 

651 
659 
668 

683 
691 
700 
708 
716 

388 
400 
411 
423 
434 

419 
431 
442 
454 
465 

451 

463 
474 
486 
497 

485 
496 
508 
519 
531 
542 

531 

542 
554 
565 
577 

567 
579 
590 
602 
613 
625 

605 
616 
628 
639 
651 
662 

644 
655 
667 
678 
690 
701 

684 
696 
707 
719 
730 
743 
753 

406 
421 
436 
451 
466 

437 

452 
467 
482 
497 

469 

484 
499 
514 
529 

502 
517 
532 
547 
562 
577 

552 
567 
582 
597 
612 

588 
603 
618 
633 
648 
664 

626 
641 
656 
671 
686 
701 

665 
680 
695 
710 
725 
740 

705 
720 
735 
750 
765 
780 
795 

426 
445 
464 

• 

457 
476 
495 
514 

489 
508 
527 
546 
565 

522 
541 
560 
579 
598 
517 

576 
595 
614 
633 
650 

612 

631 
650 
669 
688 
707 

650 

669 
688 
707 
726 
745 

689 
708 
727 
746 
765 
784 

729 
748 
767 
786 
805 
824 
843 

448 
472 

479 
502 

511 
535 
558 

545 

568 
592 
615 

603 
626 
647 

639 
663 
686 
710 

677 
700 
724 
747 
771 

716 

739 
763 
786 
810 

756 
779 
803 
826 
850 
873 

446 

476 

372 

378 
384 

457 
476 
495 
515 

483 
507 

511 

489 
508 
528 
547 
566 

523 
542 
561 
580 
599 

515 
539 
563 

543 

.... 

548 
572 
597 

577 
607 

577 
596 
615 
634 
653 

613 
632 
651 
670 
689 
709 

651 

670 
689 
708 
727 
746 

689 
709 
728 
748 
766 
785 

730 
749 
768 
787 
806 
826 
845 

607 
631 
656 

641 

644 
668 
692 
716 

678 
708 



681 
705 
730 
754 

715 

745 

.... 

720 
744 
768 
793 
817 

760 
785 
809 
833 
857 
881 

754 
784 
814 

794 
824 
854 
884 

.'•'• 

690 
701 
712 
723 
733 
744 

109 


COLUMNS 


TABLE  33 


2500-  Ib.  concrete 
I'AV^  mixture 
n  =  12 

fc=870 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

P=Afe[l+(n-iyp] 
Volume  of  Hooping  =1%  of  Volume  of  Core 

(unsupported  length\      _ 

Max.  [ —j-. —  —]  =10 

\      core  diameter      I 


Column  sire    , 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

H 

1 

IX 

1H 

H 

H 

H 

1 

IH 

IK 

"  35 
36 
37 

38 
39 
40 
41 
42 

31 
32 
33 

34 
35 
36 
37 
38 

14 
16 
18 
20 
22 
24 

14 
16 
18 
20 
22 
24 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 
30 

732 
743 
754 
765 
775 
786 

760 
774 
789 
804 
819 
833 

802 
817 
832 
846 
861 
876 

847 
861 
876 
891 
905 
920 
935 

892 
907 
922 
936 
951 
966 
980 

940 

954 
969 
984 
998 
1013 
1028 

1003 
1017 
1032 
1047 
1061 
1076 
1091 

1053 
1067 
1082 
1097 
1111 
1126 
1141 

1104 
1119 
1133 
1148 
1163 
1177 
1192 
1206 

791 
810 
829 

848 
868 
887 

834 
853 
872 
891 
910 
929 

878 
897 
916 
936 
955 
974 
993 

924 
943 
962 
981 
1000 
1020 
1039 

971 
990 
1009 
1028 
1048 
1067 
1086 

1039 
1058 
1077 
1096 
1115 
1134 
1154 

1089 
1108 
1127 
1146 
1165 
1184 
1203 

1140 
1159 
1178 
1197 
1216 
1235 
1255 
1274 

827 
851 
875 
899 
924 

866 
896 
926 

'733 

742 
750 
759 

738 
749 
761 
772 
784 
795 

780 
792 
803 
815 
826 
838 

'836 
848 
860 
871 
882 
894 

'881 
893 
905 
916 
928 
939 

'929 
941 
952 
964 
975 
987 

'989 
1001 
1012 
1024 
1035 
1047 

i039 
1051 
1062 
1074 
1085 
1097 

iio2 

1113 
1125 
1136 
1148 
1159 

762 

777 
792* 
807 
822 
837 

805 

820 
835 
850 
865 
880 

849 
864 
879 
894 
909 
925 
940 

895 
910 
925 
940 
955 
970 
985 

942 

957 
972 
987 
1002 
1017 
1032 

1006 
1021 
1036 
1051 
1066 
1081 
1096 

1056 
1071 
1086 
1101 
1116 
1131 
1146 

1107 
1122 
1137 
1152 
1167 
1182 
1197 
1212 

790 

809 
828 
847 
866 
885 

833 

852 
871 
890 
909 
928 

877 
896 
915 
934 
953 
972 
991 

923 

942 
961 
980 
999 
1018 
1037 

970 
989 
1008 
1027 
1046 
1065 
1084 

1038 
1057 
1076 
1095 
1114 
1133 
1152 

1088 
1107 
1126 
1145 
1164 
1183 
1202 

1139 
1158 
1177 
1196 
1215 
1234 
1253 
1272 

821 
845 
868 
892 
915 
939 

864 
888 
911 
935 
958 
982 

909 
932 
956 
979 
1002 
1026 
1049 

954 
978 
1001 
1025 
1048 
1072 
1095 

1001 
1025 
1048 
1072 
1095 
1119 
1142 

1073 
1097 
1120 
1144 
1167 
1191 
1214 

1123 
1147 
1170 
1194 
1217 
1241 
1264 

1175 
1198 
1222 
1245 
1269 
1292 
1316 
1339 

869 
893 
918 
942 
966 
990 

914 
938 
962 
986 
1011 
1035 
1060 

959 
984 
1008 
1032 
1056 
1081 
1105 

1007 
1031 
1055 
1079 
1103 
1128 
1152 

1079 
1104 
1128 
1152 
1176 
1200 
1225 

1129 
1154 
1178 
1202 
1226 
1250 
1275 

1180 
1205 
1229 
1253 
1277 
1302 
1326 
1350 

909 
939 
969 
999 

953 

983 
1013 
1043 

999 
1029 
1059 
1089 
1119 

1046 
1076 
1106 
1136 
1166 
1196 

1125 
1155 
1185 
1215 
1244 
1274 

'•••• 

.... 

1175 
1205 
1234 
1264 
1294 
1324 

1226 
1256 
1286 
1316 
1346 
1375 
1405 

110 


TABLE  33 


Column  size    » 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Volume  of  Hooping 


/unsupported  length\ 
Max.  [ 

\ 


1%  of  Volume  of  Core 
10 


—j-. 
core  diameter      I 


2500 -Ib.  concrete 
1:4%  mixture 
n=12 
fc=870 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

y* 

1 

1H 

IK 

H 

H 

y* 

1 

1H 

IK 

43 
44 

45 

46 
47 
48 
49 
50 

39 
40 

41 
42 
43 
44 
45 
46 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

20 
22 
24 
26 
28 
30 

1157 
1171 
1186 
1200 
1215 
1230 
1244 
1259 

1192 
1212 
1231 
1250 
1269 
1288 
1307 
1326 

1246 
1266 
1285 
1304 
1323 
1342 
1361 
1380 

1321 
1340 
1359 
1378 
1397 
1417 
1436 

1378 
1397 
1416 
1435 
1454 
1473 
1492 

1436 
1455 
1474 
1493 
1512 
1531 
1551 

1495 
1514 
1533 
1553 
1572 
1591 
1610 

1556 
1575 
1594 
1613 
1632 
1652 
1671 

1637 
1656 
1676 
1695 
1714 
1733 

1233 
1257 
1282 
1306 
1330 
1354 
1378 
1403 

1287 
1311 
1335 
1360 
1384 
1408 
1432 
1457 

1367 
1391 
1415 
1439 
1464 
1488 
1512 

1423 
1448 
1472 
1496 
1520 
1544 
1569 

1481 
1506 
1530 
1554 
1578 
1603 
1627 

1541 
1565 
1589 
1614 
1638 
1662 
1686 

1602 
1626 
1650 
1674 
1699 
1723 
1747 

1688 
1712 
1736 
1761 
1785 
1809 

1279 
1308 
1338 
1368 
1398 
1428 
1458 
1488 

1332 
1362 
1392 
1422 
1452 
1482 
1512 
1542 

1418 
1448 
1478 
1508 
1537 
1567 
1597 

1474 
1504 
1534 
1564 
1594 
1624 
1654 

1533 
1562 
1592 
1622 
1652 
1682 
1712 

1592 
1622 
1652 
1682 
1712 
1742 
1771 

1653 
1683 
1713 
1743 
1772 
1802 
1832 

1745 
1775 
1805 
1835 
1865 
1894 

1160 
1175 
1190 
1205 
1220 
1235 
1250 
1265 

1214 
1229 
1244 
1259 
1274 
1289 
1304 
1319 

1284 
1299 
1314 
1329 
1344 
1359 
1374 

1341 
1356 
1371 
1386 
1401 
1416 
1431 

1192 
1211 
1230 
1249 
1268 
1287 
1306 
1325 

1245 
1264 
1283 
1303 
1322 
1341 
1360 
1379 

1320 
1339 
1358 
1377 
1396 
1415 
1434 

1377 
1396 
1415 
1434 
1453 
1472 
1491 

1435 
1454 
1473 
1492 
1511 
1530 
1549 

1494 
1513 
1532 
1551 
1570 
1589 
1608 

1555 
1574 
1593 
1612 
1631 
1650 
1669 

1636 
1655 
1674 
1693 
1712 
1731 

1227 
1251 
1274 
1298 
1321 
1345 
1368 
1392 

1281 
1305 
1328 
1352 
1375 
1399 
1422 
1446 

1360 
1384 
1407 
1431 
1454 
1478 
1501 

1417 
1440 
1464 
1487 
1511 
1534 
1558 

1475 
1498 
1522 
1545 
1569 
1592 
1616 

1534 
1558 
1581 
1605 
1628 
1652 
1675 

1595 
1619 
1642 
1666 
1689 
1712 
1736 

1681 
1704 
1728 
1751 
1775 
1798 

1154 
1166 
1177 
1189 
1200 
1212 

:::: 

1225 
1240 
1254 
1269 
1284 
1298 
1313 

1281 
1295 
1310 
1325 
1339 
1354 
1368 

i352 
1366 
1381 
1396 
1410 
1425 

iiio 

1425 
1438 
1454 
1469 
1483 

1469 
1484 
1499 
1513 
1528 
1543 

i220 
1231 
1243 
1254 
1266 

1275 
1287 
1298 
1310 
1321 

.... 

'.'.:: 

1343 
1355 
1366 
1378 

.... 

1413 
1425 
1436 

1414 
1429 
1444 
1459 
1474 
1489 

'.'.'.'. 

i472 
1484 
1495 

1473 
1488 
1503 
1518 
1533 
1548 

1545 
1560 
1574 
1589 
1603 

1549 
1564 
1579 
1594 
1609 

•••• 

1545 
1556 

.... 

1607 
1622 
1636 
1651 
1666 

.... 

1611 
1626 
1641 
1656 
1671 

ieo7 

1618 

111 


COLUMNS 


TABLE  34 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


3000-  Ib.  concrete 
1:3  mixture 
n  =  10 


-p 

Volume  of  Hooping  =1%  of  Volume  of  Core 
Max  /unsupported  length\ 
\      core  diameter      ) 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

% 

1 

IK 

U4 

H 

H 

H 

1 

1H   1>4 

12 
13 

14 
15 

16 
17 
18 

19 
20 
21 
22 
23 

24 
25 

8 
9 

10 
11 

12 
13 
14 

15 
16 

17 
18 
19 

20 
21 

6 

6 

8 

6 

8 

6 
8 
10 

6 
8 
10 

6 
8 
10 

6 
8 
10 
12 

6 
8 
10 
12 

8 
10 
12 
14 

8 
10 
12  - 
14 

8 
10 
12 
14 

8 
10 
12 
14 
16 

8 
10 
12 
14 
16 

10 
12 
14 
16 

70 

84 
90 

100 
105 

117 
123 
129 

136 
142 
148 

157 
163 
168 

179 
185 
191 
196 

203 

209 
215 
220 

234 
240 
246 
252 

262 
267 
273 
279 

107 

125 
133 

144 
152 
161 

164 
173 

181 

187 
195 
203 
212 

211 
219 
227 
236 

245 

253 
.  261 
271 

272 
280 
289 
298 

301 
309 
317 
327 

331 
339 
348 
357 
364 

363 
372 
380 
389 
397 

405 
414 
423 
431 

134 
153 

173 

185 

196 
207 

218 

219 
231 
242 

257 
268 
279 

284 
295 
307 
318 

313 
324 
335 
347 

343 
355 
366 
377 
389 

375 
387 
398 
409 
421 

421 
432 
443 
455 

184 
206 

230 
245 

271 
285 

298 
313 

327 
341 
356 

357 
372 
387 
402 

389 
404 
419 
434 
449 

438 
453' 
468 
482 

218 
242 
286 
314 

342 
361 

373 
392 

405 
424 
443 

458 
476 

360 
390 

423 
446 

480 

89 

105 
112 

122 
129 

132 

141 

148 
156 

161 
169 
176 

184 
191 
199 
206 

208 
215 
222 
230 

241 
248 
255 
263 

268 
275 
283 
290 

297 
304 
312 
319 

327 
335 
342 
349 
357 

359 
367 
374 
382 
389 

401 
408 
415 
423 

151 
161 

171 
182 

193 
204 
215 

217 
228 
239 
249 

243 

254 
264 
275 

281 
292 
302 
313 

310 
320 
331 
342 

340 
351 
361 
372 
383 

372 
383 
394 
404 
415 

417 
428 
438 
449 

183 

205 
219 

218 

229 
243 

242 

269 

284 

287 

296 
311 

314 

.... 

325 

340 
354 

356 
370 
384 
399 

343 
362 

373 
392 

363 
393 

296 
302 
308 

'327 
332 
338 
344 

'365 
371 
376 

'399 
404 
410 

388 
402 
417 
431 
446 

436 
451 
465 
479 

406 
424 
443 

426 
450 

448 

458 
477 

483 

112 


TABLE  34 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Volume  of  Hooping  =1%  of  Volume  of  Core 


)p] 
Vol 


Max. 


/unsupported  length\ 
\       core  diameter      ) 


10 


3000 -Ib.  concrete 
1:3  mixture 
n  =  10 
fc=1050 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

K 

H 

« 

1 

IK 

IK 

H 

H 

H 

1 

1H 

IK 

2(3 
27 
28 
29 

30 
31 

32 
3.3 
34 

22 
23 
24 
25 

26 

27 

28 
29 
30 

10 
12 
14 
16 

18 

10 
12 
14 
16 

18 

10 
12 
14 
16 

18 

10 
12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 
24 

436 
443 
451 
458 
466 

452 
463 
474 
484 
495 

489 
500 
511 
521 
532 

528 
539 
549 
560 
571 

569 
579 
590 
601 
611 
622 

621 
632 
643 
653 
664 

665 
676 
686 
697 
708 
718 

710 

721 
732 
742 
753 
764 

757 

768 
779 
789 
800 
810 

'817 
827 
838 
849 
859 
870 

471 
486 
500 
515 
529 

509 
523 
538 
552 
567 

547 
562 
576 
591 
605 

588 
602 
617 
631 
646 
660 

644 
659 
673 
688 
702 

688 
703 
717 
731 
746 
760 

733 

748 
762 
777 
791 
806 

780 
795 
809 
824 
838 
853 

829 
844 
858 
872 
887 
901 
916 

494 
513 
531 

519 
543 



441 

449 
458 
466 
474 

478 
487 
496 
503 
511 

"525 
534 
542 
550 

456 
467 
479 
490 
501 

493 
504 
516 
527 
539 

532 
543 
555 
566 
577 

572 

584 
595 
606 
618 
629 

626 
637 
648 
660 
671 

669 
681 
692 
704 
715 
726 

715 

726 
738 
749 
760 
772 

762 
773 
784 
796 
807 
819 

810 

822 
833 
845 
856 
867 
879 

473 

488 
503 
518 
533 

511 
525 
540 
555 
570 

549 
564 
579 
594 
609 

590 
605 
619 
634 
649 
664 

647 
661 
67Q 
691 
706 

690 
705 
720 
735 
750 
765 

736 
751 
765 
780 
795 
810 

783 
797 
812 
827 
842 
857 

831 

846 
861 
876 
891 
906 
920 

493 
512 
531 

530 
549 
568 
587 

569 
588 
607 
625 
644 

609 
628 
647 
666 
685 

670 
689 
708 
727 
745 

714 
733 
752 
770 

789 
808 

759 

778 
797 
816 
834 
853 

806 
825 
844 
863 
881 
900 

855 
874 
893 
911 
930 
949 
968 

515 
538 

552 
575 

591 
614 
637 

631 

655 
678 
701 

697 
720 
743 

740 

764 
787 
810 

786 
809 
832 
855 
879 

833 
856 
879 
902 
925 

881 
905 
928 
951 
974 
997 



440 
445 
451 

531 

550 
569 

587 

556 

580 

584 

570 

588 
607 
626 
645 

610 
629 
648 
667 
686 

595 
619 
642 

635 
659 
683 

623 

663 
693 

!  



566 
575 
582 
591 
599 

608 
617 
624 
633 
641 

671 
690 
709 
728 
746 

715 
734 
752 

771 
790 
809 

760 
779 
798 
817 
836 
854 

807 
826 
845 
864 
883 
901 

856 
875 
893 
912 
931 
950 
969 

701 

725 
749 

745 
769 
793 
817 

790 
814 
838 
862 

837 
861 
885 
909 
933 

886 
910 
934 
958 
981 
1005 

735 

.... 

778 
808 



.... 

661 
668 
676 
685 
693 

'706 
713 
722 
730 
738 

760 
769 

777 
785 

824 
853 

871 
900 
930 

919 
949 
979 
1008 

'.'.'.'. 

809 
817 
826 
834 
842 

.... 

113 


COLUMNS 


TABLE  34 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


.^Column  sire    ^ 


3000 -lb.  concrete 
1:3  mixture 
n  =  10 
fc=1050 


Volume  of  Hooping  =1%  of  Volume  of  Core 

M      I  unsupported  length\  =lg 

\       core  diameter      I 


Size 
of 

Diameter 
of 

Number 

Squar 

e  rods 

Roun< 

irods 

column 
(.inches) 

core 
(inches) 

of 
rods 

H 

H 

K 

1 

IK 

IK 

^ 

H 

K 

1 

1H 

IK 

35 

31 

14 

867 

894 

925 

960 

999 

872 

896 

924 

955 

16 

878 

908 

944 

984 

1029 

883 

911 

943 

978 

18 

888 

923 

963 

1008 

1058 

'868 

895 

926 

962 

1001 

20 

899 

937 

982 

1032 

877 

906 

941 

980 

1024 

22 

909 

952 

1000 

1056 

884 

918 

956 

999 

1048 

24 

920 

966 

1019 



893 

929 

971 

1018 

1071 

36 

32 

14 

946 

977 

1012 

1051 

924 

948 

976 

1007 

16 

960 

996 

1036 

1081 

935 

963 

995 

1030 

18 

975 

1015 

1060 

1110 

947 

978 

1014 

1053 

20 

989 

1033 

1084 

1140 

958 

993 

1032 

1076 

22 

1004 

1052 

1108 

969 

1008 

1051 

1100 

24 

1018 

1071 

1131 

981 

1023 

1070 

1123 

37 

33 

14 

999 

1030 

1066 

1105 

1002 

1030 

1060 

16 

1014 

1049 

1089 

1135 

'989 

1017 

1048 

1084 

18 

1028 

1068 

1113 

1164 

1000 

1032 

1067 

1107 

20 

1043 

1087 

1137 

1193 

1012 

1047 

1086 

1130 

22 

1057 

1106 

1161 

1023 

1061 

1105 

1153 

24 

1072 

1125 

1185 

1034 

1076 

1124 

1176 

26 

1086 

1144 

1209 

1046 

1091 

1142 

1200 

38 

34 

14 

1055 

1086 

1121 

1160 

1057 

1085 

1116 

16 

1069 

1105 

1145 

1190 

1044 

1072 

1104 

1139 

18 

1084 

1123 

1169 

1219 

1056 

1087 

1122 

1162 

20 

1098 

1142 

1192 

1249 

1067 

1102 

1141 

1185 

22 

1112 

1161 

1216 

1278 

1078 

1117 

1160 

1208 

24 

1127 

1180 

1240 

1090 

1131 

1179 

1232 

26 

1141 

1199 

1264 

1101 

1146 

1198 

1255 

39 

35 

14 

1111 

1143 

1178 

1217 

1114 

1142 

1173 

16 

1126 

1161 

1202 

1246 

iioi 

1129 

1161 

1196 

18 

1140 

1180 

1225 

1276 

1112 

1144 

1179 

1219 

20 

1155 

1199 

1249 

1306 

1124 

1159 

1198 

1242 

22 

1169 

1218 

1273 

1335 

1135 

1173 

1217 

1265 

24 

1184 

1237 

1297 

1365 

1147 

1188 

1236 

1289 

26 

1198 

1256 

1321 

1158 

1203 

1254 

1312 

40 

36 

16 

1185 

1220 

1260 

1305 

1188 

1219 

1254 

18 

1199 

1239 

1284 

1335 

ii7i 

1202 

1238 

1278 

20 

1213 

1258 

1308 

1364 

1182 

1217 

1257 

1301 

22 

1228 

1277 

1332 

1394 

1194 

1232 

1275 

1324 

24 

1242 

1296 

1356 

1423 

1205 

1247 

1294 

1347 

26 

1257 

1315 

1380 

1453 

1217 

1262 

1313 

1370 

28 

1271 

1333 

1404 

1228 

1277 

1332 

1394 

41 

37 

16 

1245 

1280 

1320 

1365 

1248 

1279 

1315 

18 

1259 

1299 

1344 

1395 

i23i 

1263 

1298 

1338 

20 

1274 

1318 

1368 

1424 

1243 

1277 

1317 

1361 

22 

1288 

1337 

1392 

1454 

1254 

1292 

1336 

1384 

24 

1303 

1356 

1416 

1483 

1265 

1307 

1354 

1407 

26 

1317 

1375 

1464 

1513 

1277 

1322 

1373 

1430 

28 

1332 

1394 

1488 

1288 

1337 

1392 

1454 

42 

38 

16 

1307 

1342 

1382 

1427 

1310 

1341 

1376 

18 

1321 

1361 

1406 

1457 

1324 

1360 

1400 

20 

1336 

1380 

1430 

1486 

1304 

1339 

1379 

1423 

22 

1350 

1399 

1454 

1516 

1316 

1354 

1397 

1446 

24 

1364 

1418 

1478 

1545 

1327 

1369 

1416 

1469 

26 

1379 

1437 

1502 

1575 

1339 

1  384 

1435 

1492 

28 

1393 

1455 

1526 

1605 

1350 

1398 

1454 

1516 

30 

1408 

1474 

1550 

1361 

1413 

1473 

1539 

114 


TABLE  34 

^Column  si 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 


p 

Volume  of  Hooping  =1%  of  Volume  of  Core 
._       / 

'  \ 


unsupported  length\  _ 
core  diameter      ) 


3000-lb.  concrete 
1:3  mixture 
/i  =  10 
fc=1050 


Size 
of 

column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods- 

Round  rods 

*A 

H 

H 

1  i  1W 

IK 

M 

H 

H 

1 

IK  i  IK 

43 
44 

45 
46 
47 

48 
49 
50 

39 
40 

41 
42 
43 
44 
45 
46 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

20 
22 
24 
26 
28 
30 

1370 
1385 
1399 
1414 
1428 
1442 
1457 
1471 

1450 

1464 
1479 
1493 
1508 
1522 
1536 

1517 
1531 
1545 
1560 
1574 
1589 
1603 

1599 
1614 
1628 
1643 
1657 
1672 

ie7o 

1684 
1698 
1713 
1727 
1742 

l74i 
1756 
1770 
1785 
1799 
1814 

i829 
1844 
1858 
1873 
1887 

1904 
1919 
1933 
1948 
1962 

1406 
1424 
1443 
1462 
1481 
1500 
1519 
1538 

1471 
1490 
1508 
1527 
1546 
1565 
1584 
1603 

1556 
1575 
1594 
1613 
1632 
1651 
1670 

1625 
1644 
1663 
1681 
1700 
1719 
1738 

1695 
1714 
1733 
1752 
1771 
1789 
1808 

1767 
1786 
1804 
1823 
1842 
1861 
1880 

1840 
1859 
1878 
1897 
1916 
1935 
1953 

1934 
1953 
1972 
1991 
2010 
2029 

1446 
1470 
1494 
1517 
1541 
1565 
1589 
1613 

1511 
1535 
1559 
1583 
1606 
1630 
16.54 
1678 

1602 
1626 
1649 
1673 
1697 
1721 
1745 

1670 
1694 
1718 
1742 
1766 
1790 
1813 

1740 
1764 
1788 
1812 
1836 
1860 
1884 

1812 
1836 
1860 
1884 
1907 
1931 
1955 

1885 
1909 
1933 
1957 
1981 
2005 
2029 

1984 
2008 
2032 
2056 
2080 
2104 

1491 
1520i 
1550 
1579 
1609 
1638 
1668 
1697 

1556 
1585 
1615 
1644 
1674 
1703 
1733 
1762 

1652 
1682 
1711 
1741 
1770 
1800 
1829 

1720 
1750 
1780 
1809 
1839 
1868 
1898 

1791 
1820 
1850 
1879 
1909 
1938 
1968 

1862 
1892 
1921 
1951 
1980 
2010 
2039 

1936 
1965 
1995 
2024 
2054 
2083 
2113 

2040 
2070 
2099 
2129 
2159 
2188 

i368 
1379 
1391 
1402 
1413 
1425 

1373 
1388 
1403 
1418 
1432 
1447 
1462 
1477 

1438 
1453 
1468 
1483 
1498 
1512 
1527 
1542 

1520 
1535 
1550 
1564 
1579 
1594 
1609 

1588 
1603 
1618 
1633 
1648 
1662 
1677 

1(373 
1688 
1703 
1718 
1733 
1747 

i745 
1760 
1775 
1790 
1804 
1819 

1405 
1423 
1442 
1461 
1480 
1499 
1517 
1536 

1470 
1489 
1507 
1526 
1545 
1564 
1582 
1601 

1555 
1574 
1593 
1612 
1631 
1649 
1668 

1624 
1643 
1661 
1680 
1699 
1718 
1736 

1694 
1713 
1731 
1750 
1769 
1788 
1807 

1766 
1784 
1803 
1822 
1841 
1860 
1879 

1839 
1858 
1877 
1895 
1914 
1933 
1952 

1933 
1952 
1970 
1989 
2008 
2027 

1440 
1463 
1486 
1509 
1533 
1556 
1579 
1602 

1505 
1528 
1551 
1575 
1598 
1621 
1644 
1667 

1595 
1618 
1641 
1665 
1688 
1711 
1734 

1663 
1687 
1710 
1733 
1756 
1779 
1803 

1734 
1757 
1780 
1803 
1826 
1850 
1873 

1805 
1828 
1852 
1875 
1898 
1921 
1944 

1879 
1902 
1925 
1948 
1971 
1995 
2118 

1977 
2000 
2023 
2047 
2070 
2093 

'.'.'.'. 

••-• 

i444 
1456 
1467 
1479 
1490 

.  .*.  . 

isii 

1523 
1534 
1545 
1557 

::: 

is9i 

1602 
1614 
1625 

.... 

1673 
1684 
1695 

i744 
1756 
1767 

'.'.'.'. 

:::: 

— 

1833 

1848 
1863 
1878 
1893 

i908 
1923 
1938 
1953 
1968 

1829 
1840 

| 

:::: 

i904 
1915 

115 


COLUMNS 


TABLE  35 


2000-  Ib.  concrete 
1:6  mixture 
n  =  15 
fc=500 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


=  Afc[(l+4np'}+(n-l}p] 
/unsupported  length\ 
\  diameter  / 


.  Column  Size 


Size 
of 
column 
inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 

(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

H 

K 

M 

1 

1H 

IK 

12 

8 

6 

1M 

1 

6 

53 

13 

9 

5 

1M 

1 

6 

8 

64 

68 

14 

10 

4 

IH 

1 

6                76 
8                80 

81 

15 

11 

3 

1*8 

1 

6 

8     - 
10 

89 
93 
97 

95 
101 

101 

16 

12 

2 

3/0 

^K 
l$i 

1 
2 

6 

8 
10 

6 
8 
10 

103 
108 
112 

'i42 
146 

109 
115 
121 

143 
149 
155 

116 

150 

17 

13 

1 

4/0 

IK 
1% 

1 
2 

6 
8 
10 

6 
8 
10 

119 
123 

128 

'l67 

125 
131 
137 

165 
171 
177 

131 
140 

171 
180 

139 
179 

18 

14 

1 

4/0 

IK 

IK 

1 
2 

6 
8 
10 
12 

6 
8    ' 
10 
12 

136 
140 
145 
149 

142 
148 
154 
160 

148 
157 
165 

195 
203 
211 

156 

202 

'i6i 

195 

194 

200 
206 

19 

15 

0 

5/0 

1% 

1% 

1 

2 

6 
8 
10 
12 

6 
8 
10 
12 

154 
159 
163 
167 

'220 

160 
166 
172 

178 

'2ig 

225 
231 

166 
175 
183 

220 
228 
236 

174 
185 

227 
238 

183 
236 

20 

16 

2/0 

6/0 

2H 

2 

1 
2 

Q 

10 
12 
14 

8 
10 
12 
14 

178 
182 
187 
191 

'251 

186 
192 
198 
204 

'252 

258 
265 

195 
203 
211 

255 
263 
272 

205 
216 

265 
276 

217 

277 

116 


TABLE  35 


COLUMNS 


Column  size    > 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P  =  Afe[(l+4np')  +  (n- 

._       /unsupported  length\      ,_ 

Max.  [  --  —  —  —  —I  =15 

\  diameter  / 


2000 -Ib.  concrete 
1:6  mixture 
n  =  15 
fc=500 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

H 

H 

H 

1 

1H 

1H 

2  1 

17 

2/0 
6/0 

2 
I« 

1 
2 

8 
10 
12 
14 

8 
10 
12 

14 

199 
203 
207 
212 

206 
213 
219 
225 

215 

224 
232 
241 

283 
292 
300 
309 

226 
237 

294 
305 

237 
305 

.... 

'287 
293 

22 

18 

3/0 

7/0 

2H 
2 

1 
2 

8 
10 
12 
14 

8 
10 
12 
14 

8 
10 
12 
14 
16 

8 
10 
12 
14 
16 

'225 
229 
234 

228 
235 
241 
247 

'317 
323 

237 
246 
254 
263 

'322 
330 
339 

248 
259 
270 

324 
335 
346 

259 
273 

336 
350 

272 
349 

23 

19 

3/0 
7/0 

2K 
1« 

1 
2 

'248 
253 
257 
261 

252 
258 
264 
270 
276 

'355 
361 

260 
269 
277 
286 
294 

'354 
362 
370 
379 

271 
282 
293 
304 

356 
367 
378 
389 

282 
296 

368 
381 

296 
381 

24 

20 

3/0 

7/0 

2 

m 

1 
2 

8 
10 
12 
14 
16 

8 
10 
12 
14 
16 

277 
281 
286 

276 
282 
288 
295 
301 

'395 

285 
293 
302 
310 
319 

396 
405 
413 

295 
306 
317 
328 
339 

390 
401 
412 
423 
434 

307 
321 
335 

401 
415 
429 

320 
337 

414 
432 

25 

21 

4/0 

7/0 

2X 

IH 

1 
2 

10 
12 
14 
16 

10 
12 
14 
16 

'303 
307 
311 

308 
314 
320 
327 

319 
328 
336 
344 

'432 
440 

448 

332 
343 
354 
365 

436 
447 
458 
469 

347 
361 

451 
465 

363 

467 

430 

117 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


L.  Column  size    > 


2000 -Ib.  concrete 
1:6  mixture 
n=15 
fc=500 


/unsupported  length\ 

v   I  -  ^  ~  -  —  ~    I 

V  diameter  / 


Spirals                           Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
~r 



column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

UI 

Per  cent     rods 
of  core 

[I 

H 

H 

H 

1 

1H 

IK 

26 

22 

4/0 

2H 

1 

10 

335 

346 

359 

374 

390 

12 

.... 

341 

355 

370 

387 

407 

14 

334 

347 

363 

381 

401 

16 

338 

354 

371 

392 

18 

343 

360 

380 

403 

7/0      \Y% 

2 

10 

473 

488 

504 

12 

484 

502 

521 

14 

'477 

495 

516 

16     

485 

506 

18    i  

474 

494 

517 

27 

23 

4/0 

2K 

1           10 

363 

374 

387 

402 

418 

12     .... 

370 

383 

398 

416 

435 

14 

362 

376 

391 

409 

430 

16 

367 

382 

400 

420 

444 

18      371    388 

408 

431 

7/0 

1H 

2           10 

i  527 

543 

* 

12     

523 

540 

560 

14 

'516 

534 

554 

16 

524 

545 

568 

18 

.... 

533 

556 

28 

24        4/0 

2       1           10                 404 

417 

431 

448 

12 

j  :   399    412 

428 

445 

465 

14 

405 

421 

439 

459 

482 

16 

'396 

411 

429 

450 

473 

18 

401 

418 

438 

461 

487 

7/0 

\y,    2       10 

567 

584 

12 

.... 

'564 

581 

601 

14 

575 

595 

618 

16 

565    586 

609 

18 

573 

597 

623  j 

29 

25        5/0 

2M 

1           10 

435 

448 

462 

479 

12    I  

'436 

443 

459 

476 

496 

14 

436 

452 

470 

490 

513 

16 

427 

442 

460 

481 

504 

530 

18 

431 

448 

468 

492 

20 

436 

455 

477 

504 

7/0 

1H 

2 

10 

609 

626 

12 

623 

643 

14 

'eii? 

637 

660 

16     

.... 

628 

651 

677 

18   

616 

639 

665 

20 

624 

650 

30 

26 

5/0 

2H 

1           12 

462 

475 

491 

508 

528 

14 

468 

484 

502 

522 

545 

16 

474 

492 

513 

536 

562 

18 

'463 

480 

500 

524 

550 

20 

468 

487 

509 

535 

564 

7/0 

1H 

1.93        12 

656 

676 

14 

'650 

670 

693 

16 

661 

684 

710 

18 

'649 

672 

698 

20 

657 

683 

712 

118 


TABLE  35 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P=Afc((l+4np' 

(unsupported  length\ 
MaX'(  --  diameter  -  )  =15 


2000-lb.  concrete 
1:6  mixture 
n  =  15 
fc=500 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(.inches) 

Per  cent 
of  core 

y* 

« 

H 

1 

IK  |  IK 

31 

27 

5/0 
7/0 

2H 
IK 

1 
1.86 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

501 
505 

5oi 

508 
514 
520 
526 

509 
517 
525 
534 
542 
550 

524 
535 
546 
557 
568 
579 

"683 
694 
705 
716 
727 

542 
555 
569 
583 
597 
611 

689 
703 
717 
731 
745 
759 

561 
578 
595 
613 

709 
726 
743 

760 

"682 
690 
698 

32 

28 

5/0 

7/0 

2 

IX 

1 

1.80 

543 
552 
560 
568 
577 
585 

559 
570 
581 
592 
603 
614 

576 
590 
604 
618 
632 
646 

723 

737 
751 
765 
779 
793 

596 
613 
630 
647 
664 

743 

760 
777 
795 
812 
829 

.  .  .  . 
'MO 

536 
542 
548 
554 
561 

.... 

717 

728 
739 
750 
761 

724 
733 

33 

29 

6/0 
7/0 

2K 

1H 

1 
1.73 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

'576 

'578 
584 
590 
596 

579 
587 
596 
604 
613 
621 

594 
605 
616 
627 
638 
649 

612 
626 
640 
654 
668 
681 

756 
770 
784 
798 
812 
826 

631 
649 
666 
683 
700 

776 
793 
810 
828 
845 

.... 

.... 

'757 
765 

761 
772 
783 
794 

34 

30 

6/0 
7/0 

9X 

iy* 

1 
1.67 

12 
14 
16 
18 
20 
22 
24 

12 
14 
16 
18 
20 
22 
24 

'ei7 

'615 
621 
627 
634 
640 

616 
624 
633 
641 
650 
658 
667 

631 
642 
653 
664 
675 
686 
697 

649 
663 
677 
691 
705 
719 
733 

791 
805 
819 
833 
847 
861 
875 

669 
686 
703 
720 
737 
755 

811 
828 
845 
862 
879 
897 

792 
800 
809 

796 
807 
818 
829 
840 

119 


COLUMNS 


TABLE  35 


2000 -lb.  concrete 
1:6  mixture 
n  =  15 
fc=500 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 

P=Afc((l+4np')+(n-l)p] 

__       /unsupported  lengtn\      ,_ 

Max.  I -=-. —  1  =.Zo 

\  diameter  / 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

_r 

1 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

or 
rods 

H 

H 

H 

1 

1H 

1H 

35 

31 

6/0 

2M 

1 

14 

662 

680 

701 

724 

16 

671 

691 

715 

741 

18 

'659 

679 

702 

729 

758 

20 

665 

687 

713 

742 

774 

22 

671 

696 

724 

756 

792 

24 

678 

704 

735 

770 

710 

7/0 

IK 

1.62 

14 

842 

864 

16 

'832 

856 

882 

18 

843 

869 

899 

20 

854 

883 

916 

22 

'837 

865 

897 

933 

24 

845 

876 

971 

950 

36 

32 

6/0 

'2 

1 

14 

702 

720 

741 

764 

16 

711 

731 

755 

781 

18 

719 

742 

769 

798 

20 

'705 

728 

753 

783 

815 

22 

711 

736 

764 

796 

832 

24 

718 

744 

775 

810 

850 

7/0 

IK 

1.57 

14 

878 

901 

16 

'869 

892 

918 

18 

880 

906 

935 

20 

891 

920 

953 

22 

'873 

902 

934 

970 

24 

881 

913 

948 

987 

37 

33 

7/0 

2H 

1 

14 

761 

782 

805 

16 

'752 

772 

796 

822 

18 

760 

783 

809 

839 

20 

'746 

768 

794 

823 

856 

22 

752 

777 

805 

837 

873 

24 

758 

785 

816 

851 

890 

26 

765 

794 

827 

865 

908 

7/0 

IK 

1.52 

14 

915 

938 

16 

929 

955 

18 

'9i7 

943 

972 

20 

928 

957 

989 

22 

'gib 

939 

971 

1007 

24 

919 

950 

985 

1024 

26 

927 

961 

999 

1041 

38 

34 

7/0 

2H 

1 

14 

803 

824 

847 

16 

'794 

814 

838 

864 

18 

802 

825 

852 

881 

20 

810 

836 

865 

898 

22 

'794 

819 

847 

879 

915 

24 

801 

827 

858 

893 

932 

26 

807 

836 

869 

907 

950 

7/0 

IK 

1.48 

14 

954 

977 

16 

968 

994 

18 

'956 

982 

1012 

20 

967 

996 

1029 

22 

978 

1010 

1046 

24 

'958 

989 

1024 

1063 

26 

966 

1000 

1038 

1080 

120 


TABLE  35 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


=  Afc[(l+4np' 
(unsupported  length\ 
(  diarnettr  ) 


2000-lb.  concrete 
1:6  mixture 
n  =  15 
fc=500 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

^ 

K 

% 

1 

IX 

IK 

39 

35 

7/0 
7/0 

IK 

i« 

1 
1.43 

14 
16 
18 
20 

26 

14 
16 
18 
20 
22 
24 
26 

.... 

'.'.'.'. 

'845 
854 
862 
871 
879 

847 
858 
869 
880 
891 
902 
913 

867 
881. 
895 
909 
923 
937 
951 

991 
1005 
1019 
1033 
1047 
1061 
1075 

890 
907 
924 
941 
959 
976 
993 

1014 
1031 
1048 
1066 
1083 
1100 
1117 

844 
850 

:::: 

995 
1003 

993 
1004 
1015 
1026 
1037 

40 

36 

7/0 
7/0 

2 

ftM 

1 

1.40 

: 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

.... 

'895 
901 

'899 
907 
915 
924 
932 

902 
913 
924 
935 
946 
957 
968 

926 
940 
953 
967 
981 
995 
1009 

1048 
1062 
1076 
1089. 
1103 
1117 
1131 

952 
969 
986 
1003 
1020 
1038 
1055 

1074 
1091 
1108 
1125 
1143 
1160 
1177 

1637 
1046 
1054 

i646 
1057 
1068 
1079 
1090 

11 

37 

7/0 
7/0 

2 

IK 

1.36 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

936 
944 
953 
961 
970 
978 

948 
959 
970 
981 
992 
1003 
1014 

i086 
1097 
1108 
1119 
1130 

971 
985 
999 
1013 
1027 
1041 
1055 

1088 
1101 
1115 
1129 
1143 
1157 
1171 

998 
1015 
1032 
1049 
1066 
1083 
1101 

1114 
1131 
1148 
1165 
1182 
1200 
1217 

*934 
941 
947 

1086 
1094 

121 


COLUMNS 


TABLE  35 


ROUND   CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


Column  size 


2000-lb.  concrete 
1:6  mixture 
n  =  15 
fc=500 


,_       /unsupported  length\ 
Max.\  -  jr;  -  -  -  I  =15 
\  diameter  / 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

• 

Number 

-r 

| 

column 
(inches) 

of  core 

(inches) 

Size  No. 

i  (A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

rods     K 

H 

K     1 

1H 

1>4 

42 

38 

7/0 

2 

1 

16 

995 

1019 

1045 

18 

1006 

1032 

1062 

20 

99i 

1017 

1046 

1079 

22 

1000 

1028 

1060 

1096 

24 

1008 

1039 

1074 

1113 

26 

988 

1017 

1050 

1088 

1131 

28 

'.'.'.'.    994 

1025 

1061 

1102 

1148 

30 

1000 

1033 

1072 

1116 

1165 

7/0 

IK 

1.32 

16 

1127 

1154 

18 

I 

1141 

1170 

20 

ii26 

1155 

1188 

22 

....  !  .  .  .  . 

1137 

1169 

1205 

24 

.... 

1148 

1183 

1222  , 

26 

ii26 

1159 

1197 

1239 

28 

1134 

1170 

1211 

1257 

30 

i  •  •  -  - 

1142 

1181 

1225 

1274 

43 

39 

7/0 

l% 

1 

16 

1044 

1067 

1093 

18 

1055 

1081 

1110 

20 

1640 

1066 

1095 

1127 

22 

1048 

1077 

1109 

1145 

24 

1057 

1088 

1123 

1162 

26 

1065 

1099 

1137 

1179 

28 

1042 

1073 

1110 

1151 

1196 

30 

'.'.'.'.   1048 

1082 

1121 

1164 

1213 

7/0 

IK 

1.29 

16 

1171 

1197 

I 

18 

1185 

1214 

j 

20 

ii7o 

1199 

1231 

22 

1181 

1213 

1249 

24 

1192 

1227 

1266 

26 

ii69 

1203 

1241 

1283 

28 

1177 

1214 

1254 

1300 

30 

1186 

1225 

1268 

1317 

44 

40 

7/0 

IH 

1 

16 

1093 

1117 

1143 

18 

1104 

1130 

1160 

20 

1115 

1144 

1177 

22 

io98 

1126 

1158 

1194 

24 

1106 

1137 

1172 

1211 

26 

1115 

1148 

1186 

1229 

28 

i692 

1123 

1159 

1200 

1246 

30 

1098 

1132 

1170 

1214 

1263 

7/0 

IX 

1.25 

16 

1211 

1237 

18 

1225 

1254 

20 

1209 

1239 

1271 

22 

1220 

1253 

1288 

24 

1231 

1266 

1306 

26 

1242 

1280 

1323 

28 

i217 

1253 

1294 

1340 

30 

1226 

1264 

1308 

1357 

122 


TABLE  36 


COLUMNS 


Ca/umn  size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P=Afc((l+4np')+(n-l)p] 

..       (unsupported  length\ 

Max.  I -=-: —  1  =15 

\  diameter  J 


2500 -Ib.  concrete 
1:4%  mixture 
n  =  12 
fc=625 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

M 

H 

K 

1 

IH 

IH 

12 

8 

6 

1M             1 

6 

59 

13                   9 

g 

1^ 

1 

6 

8 

71 
76 

14                 10 

4 

1M 

1 

6 

8 

85 
89 

91 

15                 11 

3 

IH 

1 

6 

8 
10 

100 
105 
109 

106 
112 

113 

16 

12 

2 
3/0 

IH 
IH 

1 
2 

6 
8 
10 

6 
8 
10 

117 
121 
126 

'i55 
160 

123 
129 
135 

157 
163 
169 

129 
163 

17 

13 

1 
4/0 

IX 

IK 

1 
2 

6 

8 
10 

6 
8 
10 

135 
140 
144 

'i84 

141 
147 
153 

181 
187 
193 

148 
156 

187 
196 

195 

18 

14 

4/0 

l« 
IH 

2 

6 
8 
10 
12 

6 
8 
10 
12 

155 
159 
163 
168 

'210 
214 

161 
167 
173 
179 

'2i3 
219 
225 

167 
175 
184 

213 
222 
230 

175 
221 

19 

15 

0 
5/0 

IK 

1J4 

1 
2 

6 
8 
10 
12 

6 
8 
10 
12 

176 
180 
184 
189 

"242 

182 
188 
194 
200 

'24i 
247 
253 

188 
196 
205 

241 
250 

258 

196 
207 

249 
260 

204 
258 

20 

16 

2/0 

6/0 

2H 

2 

2 

8 
10 
12 

14 

8 
10 
12 
14 

203 
207 
211 
216 

'276 

210 
216 
222 
229 

'277 
283 
289 

219 
227 
236 

279 
288 
296 

229 
240 

289 
300 

241 
301 

123 


COLUMNS 


TABLE  36 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


^Column  size 


2500-lb.  concrete 
1:4%  mixture 
n  =  12 
fc=625 


,_       (unsupported  length\  _ 

IrlttX*  I -j7 — • 7 ~-  I   — 15 

\  diameter  / 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

.  column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

H 

H 

H 

1 

IK 

IK 

21 

17 

2/0 

2 

1 

8 

227 

234 

243 

253 

265 

10 

231 

240 

251 

264 

12 

235 

246 

260 

14 

240 

253 

268 

6/0 

1% 

2 

8 

311 

321 

333 

10 

.... 

319 

332 

12 

314 

328 

• 

14 

321 

336 

22 

18 

3/0 

2^ 

1 

8 

260 

268 

279 

290 

303 

10 

'257 

266 

277 

289 

304 

12 

261 

272 

285 

300 

14 

265 

278 

293 

7/0 

2 

2 

8 

355 

366 

379 

10 

'353 

366 

380 

12 

'348 

361 

377 

14 

354 

370 

23 

19 

3/0 

2K 

1 

8 

286 

295 

305 

317 

330 

10 

'283 

293 

304 

316 

331 

12 

288 

299 

312 

327 

14 

292 

305 

320 

338 

16 

296 

311 

328 

7/0 

IK 

2 

8 

391 

402 

415 

10 

'389 

401 

416 

12 

397 

412 

14 

'390 

405 

423 

16 

396 

414 

24 

20 

3/0 

2 

1 

8 

315 

324 

334 

345 

358 

10 

321 

332 

345 

359 

375 

12 

'316 

327 

340 

355 

373 

14 

320 

333 

348 

366 

16 

324 

339 

357 

377 

7/0 

IK 

2 

8 

428 

440 

452 

10 

439 

453 

469 

12 

'435 

450 

467 

j 

14 

443 

461 

16 

434 

451 

471 

25 

21 

4/0 

ty* 

1 

10 

350 

361 

374 

388 

404 

12 

'345 

356 

369 

385 

402 

14 

349 

362 

378 

395 

16 

354 

368 

386 

406 

7/0 

ix 

2 

10 

478 

492 

508 

12 

'474 

489 

506 

14 

482 

500 

16 

473 

490 

510 

124 


TABLE  36 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P=Afc[(l+4np')+(n-l)p] 


Max. 


'unsupported  length\ 
diameter 


=  15 


2500 -Ib.  concrete 
1:4%  mixture 
n  =  12 
fc=625 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 

(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

% 

H 

H 

1 

IH 

IX 

26 

22 

4/0 
7/0 

zy* 

i% 

1 
2 

10 
12 
14 
16 

18 

10 
12 

14 
16 

18 

'38i 
385 
389 

382 
388 
394 
400 
406 

393 
401 
409 
418 
426 

405 
416 
427 
438 
449 

520 
531 
542 
552 
563 

420 
433 
447 

534 
548 
562 

435 
453 

550 
567 

524 
532 
540 

*52i 

27 

23 

4/0 
7/0 

2H 

1% 

2 

10 
12 
14 
16 

18 

10 
12 
14 
16 

18 

'4i4 

418 
422 

414 
420 
427 
433 
439 

425 
434 
442 
450 

458 

438 
449 
460 
470 
481 

452 
466 
480 
493 

576 
590 
604 
617 

468 
485 

592 
609 

I 

.'.'  : 

'566 
574 
582 

573 
584 
594 
605 

28 

24 

4/0 
7/0 

2 

IX 

1 
2 

10 
12 
14 
16 

18 

10 
12 
14 
16 

18 

460 
468 
476 
484 
493 

472 
483 
494 
505 
515 

487 
500 
514 
527 
541 

623 
637 
650 
664 
678- 

503 
519 
536 

639 
656 
673 

"452 
456 

455 

461 
467 
473 

.... 

619 
630 
641 
652 

.... 

621 
629 

29 

25 

5/0 
7/0 

Wt 

iy* 

1 
2 

10 
12 
14 
16 
18 
20 

10 
12 
14 
16 
18 
20 

'487 
492 
496 

'490 
496 
502 
508 
514 

495 
503 
512 
520 
528 
537 

508 
519 
529 
540 
551 
562 

522 
536 
549 
563 
577 

670 
683 
697 
711 
724 

686 
703 
719 
736 

..  ; 

:::: 

'676 
684 

677 
688 
699 
709 

30 

26 

5/0 

7/0 

w 

IX 

1 
1.93 

12 
14 
16 
18 
20 

12 
14 
16 
18 

20 

'529 

533 

528 
534 
540 
546 
552 

541 
549 
557 
566 
574 

556 
567 
578 
589 
599 

'715 

725 
736 
747 

573 
587 
601 
614 
628 

721 
735 

748 
762 
776 

593 
609 
626 

740 

757 
774 

.... 

.... 

'7i3 
722 

125 


COLUMNS 


TABLE  36 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


Column  Size 


2500 -lb.  concrete 
1:4%  mixture 
n  =  12 
fc=625 


/unsupported  length\ 

Max.  I  -  -j-;  -  -  -  }  =  15 

\  diameter  / 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

_  e 

column 

(inches) 

of  core 

(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

rods 

H 

H 

Ys 

1 

1H 

IK 

31 

27 

5/0 

2^ 

1 

12 

579 

594 

612 

631 

14 

'572 

587 

605 

625 

648 

16 

578 

596 

616 

639 

664 

18 

584 

604 

627 

653 

681 

20 

'572 

590 

612 

638 

666 

22 

576 

596 

621 

648 

680 

7/0 

1H 

1.86 

12 

759 

778 

14 

.... 

'753 

773 

795 

16 

764 

787 

812 

18 

'752 

774 

800 

829 

20 

760 

785 

814 

22 

768 

796 

828 

32 

28 

5/0 

2 

1 

12 

619 

634 

651 

670 

14 

ei2 

627 

645 

665 

687 

16 

618 

635 

656 

679 

704 

18 

.... 

624 

644 

666 

692 

721 

20 

630 

652 

677 

706 

738 

22 

616 

636 

660 

688 

720 

7/0 

IK 

1.80 

12 

799 

819 

14 

793 

813 

835 

16 

804 

827 

852 

18 

815 

840 

869 

20 

800 

825 

854 

886 

22 

808 

836 

868 

33 

29 

6/0 

2>i 

1 

12 

660 

675 

693 

712 

14 

669 

686 

706 

729 

16 

659 

677 

697 

720 

746 

18 

665 

685 

708 

734 

763 

20 

671 

693 

719 

747 

779 

22 

'667 

677 

702 

729 

761 

7/0 

IK 

1.73 

12 

837 

856 

14 

851 

873 

16     

'84i 

864 

890 

18 

852 

878 

907 

20 

'838 

863 

892 

924 

22 

846 

874 

905 

34 

30 

6/0 

2>i 

1 

12 

704 

719 

736 

755 

14 

712 

730 

750 

772 

16 

703 

720 

740 

763 

789 

18 

709 

728 

751 

777 

806 

20 

715 

737 

762 

791 

823 

22 

721 

745 

773 

804 

840 

24 

'705 

727 

753 

784 

718 

7/0 

IK 

1.67 

12 

878 

897 

14 

891 

914 

16 

'882 

905 

931 

18 

893 

919 

948 

20 

'878 

904 

932 

964 

22 

887 

914 

946 

981 

! 

24    

895 

925 

960 

126 


TABLE  36 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


,_       /unsupported  length\      1C 
Max.  \          —  7^  —  I  =  lo 

\  diameter 


2500-lb.  concrete 
1:4%  mixture 
n  =  12 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam-  j 
eter 

Number 

f.£ 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  &  W. 
Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

rods 

H 

K 

ft 

1 

IH 

1H 

35 

31 

6/0 

2M 

1 

14 

756 

774 

794 

816 

16 

764 

784 

807 

833 

18 

753 

772 

795 

821 

850 

20 

759 

781 

806 

835 

867 

22 

765 

789 

817 

848 

884 

24 

771 

797 

828 

862 

901 

7/0 

1H 

1.62 

14 

933 

956 

16 

'.  '.  '.  '. 

924 

947 

972 

, 

18 

935 

961 

989 

20 

946 

974 

1006 

22 

'929 

956 

988 

1023 

24 

937 

967 

1002 

1040 

36 

32 

6/0      2 

1 

14 

802 

820 

840 

862 

16 

810 

830 

853 

879 

18 

818 

841 

867 

896 

20 

'805 

827 

852 

881 

913 

22 

811 

835 

863 

894 

930 

24 

817 

843 

874 

908 

947 

7/0 

IH 

1.57 

14 

977 

999 

16 

'968 

991 

1016 

18 

979 

1004 

1033 

20 

989 

1018 

1050 

22 

"972 

1000 

1032 

1067 

24 

981 

1011 

1045 

1084 

37 

33 

7  0 

2>£ 

1 

14 

867 

887 

909 

16 

857 

878 

901 

926 

18 

866 

888 

914 

943 

20 

'852 

874 

899 

928 

960 

22 

858 

882 

910 

942 

977 

24 

864 

890 

921 

955 

994 

26 

870 

899 

932 

969 

1011 

f/0 

1M 

1.52 

14 

1020 

1042 

16 

1033 

1059 

18 

io2i 

1047 

1076 

20 

1032 

1061 

1093 

22 

iois 

1043 

1074 

1110 

24 

1023 

1054 

1088 

1127 

26 

1031 

1064 

1102 

1144 

38 

34 

7/0 

2H 

1 

14 

....  I  .... 

916 

936 

958 

16 

'906 

926 

949 

975 

18 

914 

937 

963 

992 

20 

923 

948 

977 

1009 

22 

'967 

931 

959 

990 

1026 

24 

913 

939 

970 

1004 

1043 

26 

919 

947 

980 

1018 

1059 

7/0 

iyz 

1.48 

14 

1065 

1088 

16 

1079 

1104 

18 

i067 

1093 

1121 

20 

1078 

1106 

1138 

22 

1088 

1120 

1155 

24 

1669 

1099 

1134 

1172 

26 

1077 

1110 

1147 

1189 

127 


^> 

, 

! 

COLUMNS 

] 
&    SAI 

<££-£/ 

',500  -Ib.  concrete        \J 
':4%  mixture               V 

TABLE  36 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


Column  size    ^ 


P=Afc[(l+4np')  +  (n- 


., 
max, 


(unsupported  length\ 


fc=625 


diameter 


/ 


•** 
• 

m  •••  ••*• 

V 
} 

:> 

^- 

Size 
of 
column 
(inches) 

Diam- 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

eter 
of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

H 

H 

H 

1 

IH 

U4 

39 

35 

7/0 
7/0 

2H 
IH 

1 
1.43 

14 
16  ' 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

'963 
969 

'956 
964 
973 
981 
989 
997 

966 
976 
987 
998 
1009 
1020 
1030 

986 
999 
1013 
1026 
1040 
1054 
1068 

1109 
1122 
1136 
1150 
1163 
1177 
1191 

1008 
1025 
1042 
1059 
1076 
1093 
1109 

1131 

1148 
1165 
1182 
1199 
1216 
1233 

iii2 

1120 

iiio 

1121 
1132 
1143 
1153 

40 

•0 

£, 

36 

7/0 
7/0 

2 

IH 

1 
1.40 

16 

18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

i020 
1027 

i024 
1033 
1041 
1049 
1057 

1028 
1039 
1050 
1060 
1071 
1082 
1093 

1051 
1065 
1078 
1092 
1106 
1119 
1133 

1173 
1187 
1200 
1214 
1228 
1241 
1255 

1076 
1093 
1110 
1127 
1144 
1161 
1178 

1198 
1215 
1232 
1249 
1266 
1283 
1300 

'.'.: 

lies 

1171 
1179 

ii72 
1182 
1193 
1204 
1215 

V   41 

H> 

^ 

V 
0 
* 

37 

7/0 
7/0 

'  ! 

2 

\H 

j 

1 
1.36 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

1067 
1073 
1080 

1669 
1077 
1086 
1094 
1102 
1110 

1081 
1092 
1103 
1113 
1124 
1135 
1146 

1104 
1118 
1131 
1145 
1159 
1172 
1186 

1219 
1233 
1246 
1260 
1274 
1287 
1301 

1129 
1146 
1163 
1180 
1197 
1214 
1231 

1244 
1261 
1278 
1295 
1312 
1329 
1346 

1217 
1225 

1218 
1228 
1239 
1250 
1261 

TABLE  36 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P=Afe((l+4np' 
,_       /unsupported  length\ 
Max'( diameter ) 


15 


2500 -Ib.  concrete 
1:4%  mixture 
n  =  12 
fe=625 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  &  W. 
Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

M 

H 

M 

1 

IK 

IK 

42 

38 

7/0 
7/0 

2 
1^ 

1 
1.32 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

1136 
1147 
1158 
1168 
1179 
1190 
1201 
1212 

1159 
1173 
1186 
1200 
1214 
1227 
1241 
1255 

1268 
1282 
1296 
1309 
1323 
1337 
1350 
1364 

1184 
1201 
1218 
1235 
1252 
1269 
1286 
1303 

1294 
1311 
1328" 
1345 
1362 
1378 
1395 
1412 

.... 

ii28 

1135 
1141 

1132 
1141 
1149 
1157 
1165 
1174 

.... 

1267 
1278 
1289 
1299 
1310 
1321 

i266 
1274 
1283 

43 

39 

7/0 

7/0 

IK 
IX 

1.29 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

'.  '.'. 

iiss 

1196 
1204 
1212 
1220 
1229 

1191 
1202 
1213 
1224 
1235 
1245 
1256 
1267 

1214 
1228 
1242 
1255 
1269 
1283 
1296 
1310 

1318 
1332 
1345 
1359 
1373 
1386 
1400 
1414 

1240 
1257 
1274 
1291 
1308 
1324 
1341 
1358 

1344 
1361 
1377 
1394 
1411 
1428 
1445 
1461 

'.'.'.'. 

iioo 

1196 

1317 
1327 
1338 
1349 
1360 
1371 

1316 
1324 
1333 

44 

40 

7/0 

7/0 

1H 
IX 

1 
1.25 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

!!!? 

.... 

i253 
1261 
1269 
1277 
1286 

1248 
1259 
1270 
1280 
1291 
1302 
1313 
1324 

1271 
1285 
1298 
1312 
1326 
1339 
1353 
1367 

1366 
1380 
1393 
1407 
1421 
1434 
1448 
1462 

1296 
1313 
1330 
1347 
1364 
1381 
1398 
1415 

1392 
1409 
1425 
1442 
1459 
1476 
1493 
1510 

.... 

1247 
1253 

1365 
1375 
1386 
1397 
1408 
1419 

1372 
1381 

129 


COLUMNS 


TABLE  37 


3000-lb.  concrete 
1:3  mixture 
n=12 
fc=750 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P=Afc[(l+4np')+(n-l)p] 

,_       /unsupported  length\ 

Max.  I ^-. —  I  =25 

\  diameter  I 


Column  size     * 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 

(A.S.&W. 
Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

H 

H 

K 

1 

.IM 

1H 

12 

8 

6 

IK 

1 

6      71 

13 

9 

5 

IH 

1 

6 

8 

86 
91 

14 

10 

4 

iH 

1 

6      102 

8      107 

109 

15 

11 

3 

IH 

1 

6      121 
8      126 
10      131 

127 
135 

135 

16 

12 

2 
3/0 

1% 
IH 

1 

2 

6 

8 
10 

6 
8 
10 

141 
146 
151 

'ise 

191 

147 
155 
162 

188 
195 
203 

155 

196 

17 

13 

1 

4/0 

1% 

m 

1 
2 

6 
8 
10 

6 
8 
10 

162 
167 
172 

'226 

169 
176 
184 

217 
224 
231 

177 

187 

225 
235 

186 
234 

18 

14 

1 

4/0 

1% 

iH 

1 

2 

6 
8 
10 
12 

6 
8 
10 
12 

186 
191 
196 
201 

'251 
257 

193 
200 
207 
215 

255 

263 
270 

201 
210 
220 

256 
266 
276 

210 
265 

19 

15 

0 

5/0 

1% 
i% 

1 
2 

6 
8 
10 
12 

6 
8 
10 
12 

211 
216 
221 
226 

'290 

218 
225 
233 
240 

'289 
296 
303 

226 
236 
246 

289 
299 
309 

235 

248 

299 
312 

245 
309 

20 

16 

2/0 
6/0 

2y* 

2 

1 
2 

8 
10 
12 
14 

8 
10 
12 
14 

243 
248 
254 
259 

'331 

252 
260 
267 
274 

332 
339 
347 

263 
273 
283 

335 
345 
355 

275 

288 

347 
360 

289 
361 

130 


TABLE  37 


COLUMNS 


Column 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


P=Afe((l+4np' 

/unsupported  length\ 
*  \  diameter  / 


3000-lb.  concrete 
1:3  mixture 
n  =  12 
fe=750 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
nf 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  &  W. 
Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

rods 

M 

K 

K 

1 

IK 

1H 

I        ! 

21 

17 

2/0 

2 

1 

8 

272   281 

292 

304 

318 

10 

277 

288 

302 

317 

12 

282 

296 

312 

14 

287 

303 

321 

6/0 

IK 

2 

8 

373 

385 

399 

10 

383 

398 

12 

'377 

393 

14 

385 

403 

22 

18 

3/0 

2K 

1 

8 

312 

322 

334 

348 

363 

10 

308 

319 

332 

347 

364 

12 

313 

326 

342 

360 

14 

318 

333 

352 

7/0 

2 

2 

g 

426 

440 

455 

10 

424 

439 

456 

12 

iis 

434 

452 

14 

425 

444 

23 

19 

3/0 

2K 

1 

8 

344 

354 

366 

380 

396 

10 

340 

351 

364 

379 

397 

12 

345 

358 

374 

392 

14 

350 

366 

384 

405 

16 

355 

373 

394 

7/0 

IK 

2 

8 

469 

482 

498 

10 

.... 

'466 

481 

499 

12 

476 

494 

14 

"468 

486 

507 

16 

475 

496 

24 

20 

3/0 

2 

1 

8 

378 

388 

401 

414 

430 

10 

385 

398 

413 

431 

450 

12 

379 

392 

408 

426 

447 

14 

384 

400 

418 

439 

16 

389 

407 

428 

452 

7/0 

IK 

2 

8 

514 

528 

543 

10 

527 

544 

563 

12 

'522 

540 

560 

14 

531 

553 

16 

520 

541 

566 

25 

21 

4/0 

2K 

1 

10 

421 

434 

449 

467 

486 

12 

415 

428 

444 

462 

483 

14 

420 

436 

454 

475 

16 

425 

443 

464 

488 

7/0 

1% 

2 

10 

574 

591 

610 

12 

"570 

587 

60S 

14 

579 

600 

16 

'568 

589 

613 

131 


COLUMNS 


TABLE  37 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


^Column 


)-lb.  concrete 
1:3  mixture 
n  =  12 
fc  =  750 


P=Afc[(l+4np')  +  (n- 

,_       /unsupported  length\      ,_ 

Max.  I  -  ^  -  I  =J.o 

\  diameter          / 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
_r 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 

rods 

H 

H 

H 

1 

iy* 

1M 

26 

! 
22 

4/0 

2H 

1 

10 

458 

472 

487 

504 

523 

12 

466 

481 

500 

520 

543 

14 

'457 

473 

491 

513 

537 

16 

462 

480 

501 

526 

18 

467 

488 

511 

539 

7/0 

\*A 

2 

10 

623 

641 

660 

A  /8 

12 

636 

657 

680 

14 

'628 

649 

674 

16 

.... 

638 

662 

18 

624 

648 

675 

27 

23 

4/0 

2H 

1 

10 

498 

511 

526 

543 

562 

12 

505 

521 

539 

560 

583 

14 

'497 

512 

531 

552 

576 

16 

502 

520 

541 

565 

592 

18 

507 

527 

551 

578 

7/0 

1% 

2 

10 

693 

712 

12 

688 

709 

732 

14 

680 

701 

726 

16 

690 

714 

742 

18 

700 

727 

28 

24 

4/0 

2 

1 

10 

552 

567 

584 

603 

12 

546 

562 

580 

601 

623 

14 

553 

572 

593 

617 

644 

16 

543 

560 

581 

606 

633 

18 

548 

568 

591 

619 

650 

7/0 

IK 

2 

10 

747 

766 

A/2 

12 

743 

763 

786 

14 

756 

780 

806 

16 

'744 

769 

796 

18 

754 

782 

813 

29 

25 

5/0 

2M 

1 

10 

594 

610 

627 

646 

12 

'589 

604 

623 

643 

f>60 

14 

596 

614 

636 

660 

687 

16 

'585 

603 

624 

648 

676 

707 

18 

590 

610 

634 

661 

692 

20 

595 

618 

644 

674 

7/0 

114 

2 

10 

804 

823 

•*•  /2 

12 

820 

843 

14 

'812 

836 

863 

16 

825 

853 

884 

18 

'sii 

838 

869 

20 

821 

851 

30 

26 

5/0 

2?<t 

1 

12 

633 

649 

667 

688 

711 

14 

640 

659 

680 

704 

731 

16 

648 

669 

693 

720 

751 

18 

'635 

655 

678 

706 

737 

20 

640 

662 

688 

719 

753 

7/0 

IK 

1.93 

12 

867 

890 

14 

'859 

883 

910 

16 

872 

900 

930 

18 

'858 

885 

916 

1 

20 

.... 

868 

898 

932 

132 


TABLE  37 


COLUMNS 


Column  3L2S. 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


Max. 


/unsupported  length\ 


diameter 


15 


3000-lb.  concrete 
1:3  mixture 
n  =  12 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

H 

H 

M 

1 

IK 

IK 

31 

27 

5/0 

7/0 

2K 
IK 

1 
1.86 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

686 
691 

'687 
694 
701 
708 
716 

695 
705 
715 
725 
735 
745 

713 

726 
739 
752 
765 

778 

'962 
915 
928 
941 
954 

734 
750 
767 
783 
800 
816 

910 
926 
943 
959 
976 
992 

757 

777 
797 
818 

933 
953 
974 
994 

901 
911 
921 

32 

28 

5/0 
7/0 

2 
IK 

1 
1.80 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

'739 

'735 
742 
749 
756 
764 

743 
753 
763 
773 
783 
793 

761 
774 
787 
800 
813 
826 

'956 
963 
976 
989 
1002 

782 
798 
815 
831 
848 
864 

957 
974 
990 
1007 
1023 
1039 

805 
825 
845 
866 
886 

981 
1001 
1021 
1041 
1061 

'958 
968 

33 

29 

6/0 
7/0 

2K 
l« 

1.73 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

'789 

'791 
799 
806 
813 

793 
803 
812 
822 
832 
842 

811 
824 
837 
850 
863 
876 

832 
848 
864 
881 
897 
913 

1004 
1020 
1037 
1053 
1070 
1086 

855' 
875 
895 
915 
936 

1027 
1047 
1067 
1088 
1108 

1009 
1022 
1035 
1048 

ioos 

1015 

.... 

.... 

34 

30 

6/0 

7/0 

2K 
IK 

1 
1.67 

12 
14 
16 
18 
20 
22 
24 

12 
14 
16 
18 
20 
22 
24 

844 
854 
864 
874 
884 
894 
904 

862 
875 
888 
901 
914 
927 
940 

883 
899 
916 
932 
949 
965 
981 

1053 
1069 
1086 
1101 
1118 
1135 
1151 

906 
926 
946 
967 
987 
1007 

1076 
1096 
1116 
1137 
1157 
1177 

!  .... 
'845 

843 
850 
857 
865 
872 

1058 
1071 
1084 
1097 
1110 

:::: 

:::: 

i654 
1063 
1073 

133 


COLUMNS 


TABLE  37 


3000- Ib.  concrete 
1:3  mixture 
n=12 
f c=7  50 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 

P=Afc[(l+4np'}+(n-l}p\ 
Max  /unsupported  length\ 
\  diameter  / 


Column  Size     ^ 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
I  W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

$i 

H 

H 

1 

1H 

IK 

35 

31 

6/0 

2>6 

i 

14 

907 

929 

953 

980 

16     .... 

917 

941 

969 

1000 

18    

'963 

927 

954 

985 

1020 

20 

911 

937 

967 

1002 

1040 

22 

918 

947 

980 

1018 

1061 

24 

925 

957 

993 

1035 

1081 

7/0 

1H 

].62 

14 

1123 

1150 

16 

iiii 

1139 

1170 

18 

.... 

1124 

1155 

1190 

20 

1137 

1172 

1210 

22 

iii7 

1150 

1188 

1231 

24 

1127 

1163 

1205 

1251 

36 

32 

6/0 

2 

1 

14 

962 

983 

1007 

1034 

16 

972 

996 

1024 

1055 

18 

982 

1009 

1040 

1075 

20 

'965 

992 

1022 

1056 

1095 

22 

973 

1002 

1035 

1073 

1115 

24 

980 

1012 

1048 

10.89 

1136 

7/0 

IK 

1.57 

14 

1173 

1200 

16 

ii<52 

1189 

1220 

18 

1175 

1206 

1240 

20 

1187 

1222 

1260 

22 

ii67 

1200 

1239 

1280 

\ 

24   I  .... 

1177 

1213 

1256 

1301 

37 

33        7/0 

2M 

1          14 

1040 

1064 

1091 

16     ,  

i028 

1053 

1080 

1111 

• 

18     .... 

1038 

1066 

1097 

1131 

20     .... 

1022 

1048 

1079 

1113 

1151 

22     

1029 

1058 

1092 

1130 

1172 

24 

1037 

1068 

1105 

1146 

1192 

26 

1044 

1078 

1118 

1164 

1212 

7/0 

U2 

1.52 

14 

1225 

1251 

16 

1241 

1272 

18 

i226 

1257 

1292 

20 

.... 

1239 

1274 

1312 

22 

i2ij> 

1252 

1290 

1332 

24     

1229 

1265 

1307 

1353 

26     

1239 

1278 

1323 

1373 

38 

34 

7/0 

2Y& 

1           14 

1098 

1123 

1149 

16   

io87 

1111 

1139 

1170 

18    :  .... 

1097 

1124 

1155 

1190 

20     .... 

1107 

1137 

1172 

1210 

22     .... 

1088 

1117 

1150 

1188 

1230 

24 

1095 

1127 

1163 

1205 

1251 

26 

1102 

1137 

1176 

1221 

1271 

7/0 

1>2 

1.48 

14 

1279 

1306 

16 

1296 

1326 

18 

.  .  .  . 

i2si 

1312 

1347 

20 

1294 

1328 

1367 

22 

1307 

1345 

1387 

24 

1283 

1320 

1361 

1407 

26 

1293 

1333 

1378 

1428 

134 


TABLE  S7 


COLUMNS 


ROUND  .CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


--       /unsupported  length\      ,_ 

Max.  [  -         —j-.  -  -  -       J  =  15 

\  diameter  / 


3000-lb.  concrete 
1:3  mixture 
n  =  12 
ff=750 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

i 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

K 

H 

% 

1 

IX 

1M 

39 

35 

7/0 
7/0 

2K 

l)i 

1 
1.43 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

•••• 

il47 
1157 
1167 
1177 
1187 
1197 

1158 
1172 
1185 
1197 
1210 
1223 
123G 

1183 
1199 
1216 
1232 
1248 
1265 
1281 

1334 
1351 
1367 
1383 
1400 
1416 
1433 

1210 
1230 
1250 
1270 
1291 
1311 
1331 

1361 
1381 
1402 
1422 
1442 
1462 
1483 

1148 
1155 
1163 

1336 
1349 
1362 
1375 
1388 

1339 
1348 

40 

36 

7/0 
7/0 

cy 

1H 

1.40 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

1233 
1246 
1259 
1272 
1285 
1298 
1311 

1261 
1277 
1294 
1310 
1327 
1313 
1359 

1406 
1423 
1439 
1455 
1472 
1488 
1505 

1292 
1312 
1332 
1353 
1373 
1393 
1413 

1437 
1457 
1477 
1498 
1518 
1538 
1558 

i225 
1231 

1229 
1239 
1249 
1259 
1269 

1404 
1417 
1430 
1443 
1456 

1394 
1404. 
1414 

41 

37 

7/0 
7/0 

2 

1H 

1.36 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

i2si 

1288 
1295 

.... 

i283 
1293 
1303 
1312 
1322 
1332 

i4o9 
1469 

1297 
1310 
1323 
1336 
1349 
1361 
1375 

i-iso 

1473 
I486 
1499 
1512 

1325 
1341 
1357 
1374 
1390 
1407 
1423 

1462 
1478 
1495 
1511 
1527 
1544 
1560 

1355 
1376 
1396 
1416 
1436 
1457 
1477 

1492 
1513 
1533 
1553 
1573 
1594 
1614 

135 


COLUMNS 


TABLE  37 


3000 -lb.  concrete 
1:3  mixture 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

AMERICAN  CONCRETE  INSTITUTE 

RECOMMENDATIONS 


=  Afc[(l+4np')+(n-l}p] 
(unsupported  length\  _ 
'  \  diameter          / 


Column  Size    ^ 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 



column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

H 

H 

% 

1 

IH 

IK 

42 

38 

7/0 

2 

1          16    !   ... 

1362 

1390 

1421 

18 

1375 

1406 

1441 

20 

i358 

1388 

1423 

1461 

22 

1368 

1401 

1439 

1482 

24 

1378 

1414 

1456 

1502 

26 

1354 

1388 

1427 

14*72 

1522 

28 

1360 

1398 

1440 

1488 

1542 

30 

1368 

1408 

1453 

1504 

1563 

7/0 

IK 

1.32 

16 

1520 

1551 

18 

1537 

1571 

20 

1519 

1553 

1591 

22 

1532 

1570 

1612 

24 

1545 

1586 

1632 

26 

isis 

1558 

1603 

'1652 

28 

1528 

1571 

1619 

1673 

30 

1538 

1583 

1635 

1693 

43 

39 

7/0 

iy* 

1 

16 

1430 

1457 

1488 

18 

1443 

1474 

1508 

20 

1425 

1456 

1490 

1528 

22 

1435 

1469 

1506 

1549 

24 

1445 

1482 

1523 

1569 

26 

1455 

1494 

1539 

1589 

28 

i428 

1465 

1507 

1556 

1609 

30 

1435 

1475 

1520 

1572 

1630 

7/0 

IK 

1.29 

16 

1583 

1613 

18 

1599 

1634 

20 

1581 

1615 

1654 

22 

1594 

1632 

1674 

24 

1607 

1648 

1694 

26 

isso 

1620 

1665 

1715 

28 

1590 

1633 

1681 

1735 

30 

1600 

1645 

1697 

1755 

44 

40 

7/0 

1% 

1 

16 

1498 

1526 

1557 

18 

1511 

1542 

1577 

20 

1524 

1559 

1597 

22 

is  b-4 

1537 

1575 

1618 

24 

1514 

1550 

1592 

]  638 

26 

1524 

1563 

1608 

1658 

28 

1496 

1534 

1576 

1624 

1678 

30 

1504 

1544 

1589 

1641 

1699 

7/0 

IK 

1.25 

16 

1639 

1670 

18 

1656 

1690 

20 

1(337 

1672 

1710 

22 

1650 

1688 

1731 

24 

1663 

1705 

1751 

26 

1670 

1721 

1771 

28 

1647 

1689 

1738 

1791 

30 

1657 

1702 

1754 

1812 

130 


TABLE  38 


COLUMNS 


Column  size 


ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
NEW  YORK  CITY  BUILDING  CODE 
REQUIREMENTS 

P  =Afc(l  +  (n  -l)p]  +2fsp'A 
ft=20,000 


1:6  mixture 
n  =  15 
fe=500 


Size 
of 
column 
(inches) 

Diam- 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

eter 
of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

X 

K 

H 

1 

1H 

IK 

12 

8 

6 

IK 

1 

6 

58 

13                   9                   5 

1M 

1 

6 

8 

70 

74 

14                 10 

4 

IK 

1 

6 

8 

83 

88 

89 

15                 11 

3 

IH 

1 

6 
8 
10 

98 
103 
107 

104 
110 

ill 

16 

12 

2 

3/0 

IK 
1H 

1 
2 

6 

8 
10 

6 
8 
10 

115 
119 
123 

'iei 

168 

120 
126 
133 

166 
172 
178 

127 
172 

17 

13 

1 
4/0 

IK 

IVs 

1 
2 

6 
8 
10 

6 
8 
10 

132 
137 
141 

'i94 

138 
144 
150 

191 
197 
203 

145 
153 

198 
206 

152 
205 

18 

14 

1 

4/0 

IK 
IK 

1 
2 

6 
8 
10 
•  12 

6 
8 
10 
12 

151 
156 
160 
164 

"222 
226 

157 
163 
169 
176 

'225 
231 
237 

164 
172 
181 

225 
234 
242 

171 
233 

19 

15 

0 
5/0 

Ul 
1% 

1 
2 

6 
8 
10 
12 

6 
8 
10 
12 

172 
176 
180 
185 

'255 

178 
184 
190 
196 

'254 
261 

267 

184 
193 
201 

255 
263 
272 

192 
203 

263 
274 

201 
271 

20 

16 

2/0 

6/0 

2H 
2 

1 
2 

8 
10 
12 
14 

8 
10 
12 
14 

198 
202 
207 
211 

'29i 

206 
212 
218 
224 

'292 
299 
305 

215 
223 
231 

295 
303 
312 

225 
236 

305 
316 

237 
317 

137 


COLUMNS 


TABLE  38 


1:6  mixture 
n  =  15 
fc=500 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 

-l)p]+2f,p'A 
fs=  20,000 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

column 
(inches) 

of  core 

(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

rods 

M 

M 

14 

1 

IK 

IX 

21 

17 

2/0 

0 

1 

8 

221 

229 

238 

248 

260 

10 

226 

235 

246 

259 

12 

230 

241 

255 

14 

234 

248 

263 

6/0 

114 

2 

8 

329 

339 

351 

10 

337 

350 

12 

'332 

346 

14 

338 

354 

22 

18 

3/0 

2>4 

1 

8 

254 

263 

273 

285 

298 

10 

'256 

260 

271 

284 

299 

12 

255 

266 

280 

295 

14 

259 

272 

288 

7/0 

2 

2 

8 

375 

386 

400 

10 

'373 

386 

400 

12 

'368 

381 

397 

14 

374 

390 

23 

19 

3/0 

2V& 

1 

8 

280 

289 

299 

311 

324 

10 

'277 

286 

297 

310 

325 

12 

281 

292 

306 

321 

14 

285 

298 

314 

332 

16 

289 

305 

322 

7/0 

114 

2 

8 

412 

424 

437 

10 

411 

423 

438 

12 

419 

434 

14 

'412 

427 

445 

16 

418 

436 

24 

20 

3/0 

2 

1 

8 

307 

316 

327 

338 

351 

10 

314 

325 

338 

352 

369 

12 

'308 

320 

333 

349 

366 

14 

313 

326 

342 

360 

i  ! 

16      317 

332 

350 

371 

7/0 

114 

2           8 

452 

464 

477 

10 

.  463 

478 

494 

12 

'459 

474 

492 

14 

467 

485 

16 

'458 

476 

496 

25 

21 

4/0      2K 

1           10 

343 

354 

367 

381 

398 

12 

'337 

349 

362 

378 

395 

1 

14      342 

355 

371 

389 

16      346 

361 

379 

400 

7/0      1?4 

l'           10 

505 

520 

536 

12 

'soi 

516 

534 

14 

509 

527 

16 

500 

518 

538 

138 


TABLE  88 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


f  , 


1:6  mixture 

71=15 

fe=500 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Percent 
of  core 

K 

H 

H 

1 

I.H 

1>4 

26 

22 

4/0 
7/0 

2  ?-8 

1« 

1 
2 

10 
12 
14 
16 
18 

10 
12 
14 
16 

18 

'372 
376 
381 

373 

379 
385 
391 
398 

384 
393 
401 
409 
418 

397 
408 
419 
430 
441 

549 
560 
571 
582 
593 

412 
425 
439 

564 
578 
592 

428 
445 

580 
597 

550 

'553 
561 
570 

27 

23 

1 

4/0 
7/0 

2H 
1^ 

2 

10 
12 
14 
16 
18 

10 
12 
14 
16 

18 

"404 
408 
413 

405 
411 
417 
423 
430 

416 
424 
433 
441 
450 

429 
440 
451 
462 
473 

443 
457 
171 
485 

610 
624 
638 
651 

460 
477 

626 
643 



'599 
607 
616 

606 
617 
628 
639 

28 

24 

4/0 
7/0 

2 

IH 

1 
2 

10 
12 
14 
16 
18 

10 
12 
14 
16 

18 

10 
12 
14 
16 
18 
20 

10 
12 
14 
16 
18 
20 

441 
446 

444 
450 
457 
463 

449 
458 
466 
474 
483 

'655 
664 

462 
473 
484 
495 
506 

'654 
665 
676 
687 

477 
491 
505 
518 
532 

658 
672 
686 
699 
713 

493 
510 
527 

674 

691 
708 

29 

25 

5/0 

7/0 

2X 

iyz 

1 
2 

'476 
480 
485 

479 
485 
491 
497 
504 

484 
492 
501 
509 
518 
526 

497 
508 
519 
530 
541 
551 

511 
525 
539 
553 
567 

708 
722 
736 
749 
763 

528 
545 
562 
579 

724 
741 

758 
776 

'714 
722 

715 
726 
737 
748 

30 

26 

5/0 
7/0 

2« 

1H 

1 
1.93 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

'sie 

521 

515 
521 
527 
533 
540 

528 
537 
545 
554 
562 

544 
555 
566 
577 
588 

'752 
763 

774 
785 

501 
575 
589 
603 

759 
773 
787 
801 
815 

581 
598 
615 

778 
796 
813 

'75i 
760 

139 


COLUMNS 


TABLE  38 


1:6  mixture 

n=15 

fc=500 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 

-l)p]+2fsp'A 
fs=20,000 
length  \ 


*  \diameterl 


=  15 


! 

Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

H 

% 

% 

1 

Ui 

1M 

31 

27 

5/0 

2V£ 

1 

12 

566 

581 

599 

618 

^7a 

14 

559 

574 

592 

613 

636 

16 

565 

583 

603 

627 

653 

18 

571 

591 

614 

641 

670 

20 

'558 

577 

599 

625 

654 

22 

563 

583 

608 

636 

668 

7/0 

1M 

1.86 

12 

796 

816 

14 

'796 

810 

833 

16 

801 

824 

850 

18 

'789 

812 

838 

868 

20 

797 

823 

852 

22 

806 

834 

866 

32 

28 

5/0 

2 

1 

12 

605 

620 

638 

657 

14 

'597 

613 

631 

652 

674 

16 

604 

622 

642 

666 

692 

18 

610 

630 

653 

679 

709 

20 

616 

638 

664 

693 

726 

22 

'eoi 

622 

647 

675 

707 

7/0 

1H 

1.80 

12 

834 

854 

14 

'827 

'  848 

871 

16 

838 

862 

888 

18 

849 

876 

905 

20 

'835 

860 

890 

922 

22 

843 

871 

904 

33 

29 

6/0 

2H 

1 

12 

645 

660 

678 

697 

14 

653 

671 

692 

715 

16 

'644 

662 

682 

706 

732 

18 

!  !  .  . 

650 

670 

693 

720 

749 

20 

656 

679 

704 

734 

766 

22 

*642 

662 

687 

715 

747 

7/0 

1H 

1.73 

12 

869 

889 

14 

883 

906 

16 

'874 

897 

923 

18 

885 

911 

940 

20 

'870 

896 

925 

958 

22 

878 

907 

939 

34 

30 

6/0 

2X 

1 

12 

687 

702 

720 

739 

14 

695 

713 

734 

756 

16 

'686 

704 

724 

748 

•774 

18 

692 

712 

735 

761 

791 

20 

698 

720 

746 

775 

808 

22 

704 

729 

757 

789 

825 

24 

'688 

710 

737 

768 

803 

7/0 

\H 

1.67 

12 

908 

928 

14 

922 

945 

16 

'913 

936 

962 

18 

924 

950 

980 

20 

909 

935 

964 

997 

22 

917 

946 

978 

1014 

24 

926 

957 

992 

140 


TABLE  38 


COLUMNS 


Column  size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 

P  =  Afe[l  +  (w  -l)p]  +2fsp'A 
f,=20,000 
I  length  \ 


Max. 


\diameteri 


=  15 


1:6  mixture 
n  =  15 
fe=500 


Size 
of 

column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

*A 

H 

H 

1 

1H 

t# 

35 

31 

6/0 
7/0 

2^ 
1H 

1 
1.62 

14 
16 
18 
20 
22 
24 

14 
16 
18 
20 
22 
24 

'735 

741 
747 
754 

738 
747 
755 
763 
772 
780 

756 

767 
778 
789 
800 
811 

777 
791 
805 
818 
832 
846 

964 
978 
992 
1006 
1020 
1033 

800 
817 
834 
851 
868 
885 

987 
1004 
1021 
1038 
1055 
1073 

954 
965 
976 
987 
998 

959 
967 

36 

32 

6/0 

7/0 

2 

IK. 

1 
1.57 

14 
16 
18 
20 
22 
24 

14 
16 
18 
20 
22 
24 

'786 
792 
798 

783 
791 
799 
808 
816 
825 

801 
812 
823 
834 
845 
856 

'994 
1005 
1016 
1026 
1038 

821 
835 
849 
863 
877 
891 

1003 
1017 
1031 
1045 
1059 
1073 

844 
861 
878 
896 
913 
930 

1026 
1043 
1060 
1078 
1095 
1112 

'999 
1007 

37 

33 

7/0 
7/0 

2tf 
1H 

1 
1.52 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

847 
858 
869 
880 
891 
902 
913 

867 
881 
895 
909 
923 
937 
951 

1043 
1057 
1071 
1085 
1099 
1113 
1127 

890 
907 
924 
942 
959 
976 
993 

1066 
1083 
1101 
1118 
1135 
1152 
1169 

.... 

'832 
838 
844 
850 

837 
845 
854 
862 
871 
879 

1045 
1056 
1067 
1078 
1089 

1039 
1047 
1055 

68 

34 

7/0 
7/0 

2H 

1>2 

1 

1.4S 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

'885 
891 
898 

.... 

'884 
893 
901 
909 
918 
927 

1692 
1100 

894 
905 
916 
927 
938 
949 
960 

1690 
1101 
1112 
1123 
1134 

915 
928 
942 
956 
970 
984 
998 

1088 
1102 
1116 
1130 
1144 
1158 
1171 

937 
955 
972 
989 
1006 
1023 
1-040 

1111 
1128 
1146 
1163 
1180 
1197 
1214 

141 


COLUMNS 


TABLE  38 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


Cofumn  size    ^ 


1:6  mixture 
n  =  15 
fc=500 


-l)p]+2fsp'A 
fs=20,000 
/   length  \ 
\diameter 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

•kT        1           ' 

Number  ~ 
nf 

column 
(inches) 

of  core 

(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

rods     ^     ^ 

7A 

1 

1H 

1>4 

39 

35        7/0      2>£ 

1           14    1  

943 

963 

986 

16     

933 

954 

977 

1003 

j  | 

18     

942 

964 

991 

1020 

20     

950 

975 

1005 

1038 

22            934 

958 

986 

1019 

1055 

24            940 

967 

997 

1033 

1071 

26   '  i   946 

975 

1008 

1047 

1089 

7/0 

\Y2      1.43        14 

1129 

1152 

16 

1143 

1169 

18     

iisb 

1157 

1187 

20     

1141 

1171 

1204 

22     

1152 

1185 

1221 

24     

iis3 

1164 

1199 

1238 

26     

1141 

1175 

1213 

1255 

40       36        7/0      2        1 

16 

1005 

1028 

1055 

18     

'992 

1016 

1042 

1072 

20     

1001 

1027 

1056 

1089 

22     

1010 

1038 

1070 

1106 

24     990 

1018 

1049 

1084 

1123 

26     997 

1027 

1060 

1098 

1140 

28           1004 

1035 

1071 

1112 

1158 

7/0 

IH 

1.40 

16 

1190 

1216 

18     

.... 

1204 

1234 

20     

iis9 

1218 

1251 

22     

1200 

1232 

1268 

24     

iisb 

1211 

1246 

1285 

26     

1188 

1222 

1260 

1302 

28     '  

1197 

1233 

1274 

1320 

41       37 

7/0 

2        1 

16 

1056 

1079 

1105 

18     

1643 

1067 

1093 

1122 

20     

1052 

1078 

1107 

1139 

22     

1060 

1089 

1121 

1157 

24     1042 

1069 

1100 

1135 

1174 

26     1048 

1077 

1111 

1149 

1191 

28     1054 

1085 

1122 

1162 

1208 

!                   , 

7/0      \K 

1.36 

16 

1233 

1259 

! 

18     

1247 

1277 

20   

1232 

1261 

1294 

22   1   1  

1243 

1275 

1311 

24     

1254 

1289 

1328 

26     

i23i 

1265 

1303 

1345 

28      

1240 

1276 

1317 

1362 

142 


TABLE  38 


COLUMNS 


Column  Size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


f,=20, 


1:6  mixture 

n=15 

fc=500 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
{.inches) 

Per  cent 
of  core 

« 

H 

y* 

1 

IX 

M 

42 

38 

7/0 
7/0 

2 
1« 

1 
1.32 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

hoi 

1107 
1113 

iios 

1113 
1122 
1130 
1138 
1147 

1109 
1120 
1131 
1142 
1153 
1164 
1175 
1186 

1132 
1146 
1160 
1174 
1188 
12D2 
1215 
1229 

1277 
1291 
1305 
1319 
1333 
1347 
1361 
1375 

1158 
1175 
1192 
1210 
1227 
1244 
1261 
1278 

1303 
1321 
1338 
1355 
1372 
1389 
1407 
1424 

1276 
1287 
1298 
1309 
1320 
1331 

1275 
1284 
1292 

43 

39 

7/0 
7/0 

IH 
IX 

1 
1.29 

11 

20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

iie2 

1168 

il59 
1168 
1176 
1185 
1193 
1201 

1163 
1174 
1185 
1196 
1207 
1218 
1229 
1240 

1186 
1200 
1214 
1228 
1242 
1256 
1270 
1284 

1323 
1337 
1351 
1365 
1379 
1392 
1407 
1421 

1212 
1230 
1247 
1264 
1282 
1298 
1316 
1333 

1349 
1367 
1384 
1401 
1418 
1435 
1453 
1470 

•••• 

i32i 
1330 
1338 

1322 
1333 
1344 
1355 
1366 
1377 

44 

40 

7/0 

7/0 

IK 
1H 

1 
1.25 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

1219 
1230 
1241 
1252 
1263 
1274 
1285 
1296 

1242 
1256 
1270 
1284 
1298 
1312 
1326 
1340 

1367 
1381 
1395 
1409 
1423 
1437 
1451 
1465 

1268 
1286 
1303 
1320 
1337 
1354 
1371 
1389 

1393 
1411 
1428 
1445 
1462 
1479 
1497 
1514 



1224 
1232 
1240 
1249 
1257 

1217 
1224 

i,374 
1382 

1366 
1377 
1388 
1399 
1410 
1421 

143 


COLUMNS 


TABLE  39 


1:4Y2  mixture 

n=12 

fc=600 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


n-l)p]+2fsp'A 
fs=20,000 

}=15 


,^  Column  size    o 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 

(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

*A 

H 

14, 

1 

1M 

Ui 

12       8 

6 

IK 

1 

6 

62 

13 

9 

5 

lYz 

1 

6 

8 

76 
80 

14       10 

4 

iy* 

1 

6 
8 

91 
95 

96 

15 

11 

3 

IK 

1 

6 
8 
10 

107 
111 
115 

112 

118 

119 

16 

12 

2 
3/0   • 

IK 
IH 

1 
2 

6 
8 
10 

6 
8 
10 

125 
129 
133 

'i75 
179 

131 
136 
142 

176 

182 
187 

J37 

182 

17 

13 

1 
4/0 

1H 
IK 

1 

2 

6 
8 
10 

6 
8 
10 

145 
149 
153 

'206 

150 
156 
162 

203 
209 
215 

157 
164 

210 

217 

164 
217 

18 

14 

1 
4/0 

1H 
1% 

1 
2 

6 

8 
10 
12 

6 

8 
10 
12 

166 
170 
174 
178 

'236 
240 

171 
177 
183 
189 

'239 
245 
250 

178 
186 
194 

239 

247 
255 

185 

247 

19 

15 

0 
5/0 

IK 
IK 

1 
2 

6 
8 
10 
12 

6 
8 
10 
12 

189 
193 
197 
201 

'272 

194 
200 
206 
212 

'27i 
276 

282 

201 
208 
216 

271 
279 
287 

208 
218 

278 
289 

216 

237 

20 

16 

2/0 

6/0 

2^ 
2 

1 
2 

8 
10 
12 
14 

8 
10 
12 
14 

217 
221 
225 
229 

'SIO 

224 
230 
236 
242 

'sii 

316 
322 

233 
241 
249 

313 
321 
329 

243 
253 

323 
333 

254 
334 

144 


TABLE  39 


COLUMNS 


Column  size    > 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 

-l)p]+2f,p'A 


f,= 


1:4]4  mixture 
n  =  12 
fc=600 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

*8 

H 

H 

1 

IK 

iy* 

21 

17 

2/0 
6/0 

2 

IK 

2 

8 
10 
12 
14 

8 
10 
12 

14 

243 
247 
251 
255 

250 
256 
262 
268 

353 
359 

259 
267 
275 
283 

350 
357 
365 
373 

268 
289 

359 
370 

279 
370 

22 

18 

3/0 

7/0 

2H 

2 

1 
2 

8 
10 
12 
14 

8 
10 
12 

14 

'275 
279 
283 

278 
284 
289 
295 

286 
294 
302 
310 

296 
306 
317 

398 
408 
419 

307 
320 

409 
422 

319 
421 

396 
404 
412 

391 
397 

23 

19 

3/0 
7/0 

2H 

IK 

1 
2 

8 
10 
12 
14 

16 

8 
10 
12 
14 
16 

*304 
308 
312 
316 

307 
313 
318 
324 
330 

315 
323 
331 
339 
347 

'437 
445 
452 
460 

325 
335 
346 
366 

438 
449 
459 
469 

336 
349 

449 
463 

348 
462 

•  •' 

'438 
444 

24 

20 

3/0 

7/0 

2 

IK 

1 
2 

8 
10 
12 
14 
16 

8 
10 
12 
14 
16 

'338 
343 
347 

337 
343 
349 
355 
361 

346 
354 
362 
370 
378 

356 
366 
376 
387 
397 

481 
492 
502 
512 
523 

367 
380 
393 

492 
505 
519 

379 
395 

505 
521 

487 
495 
503 

:::: 

'486 

25 

21 

4/0 
7/0 

2x 

'*. 

1 
2 

10 
12 
14 
16 

10 
12 
14 
16 

37i 

375 
379 

376 
381 
387 
393 

386 
394 
402 
410 

'533 
540 
548 

398 
409 
419 
429 

537 

547 
557 
568 

412 
425 

551 

564 

427 
566 

532 

145 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


1:4}^  mixture 
n  =  12 
fc=600 


fg=20,000 

I   length  \ 

Max.  (  -T-.  —       —  )  =  15 

\diameterj 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

r 

I 

^ 

column 
(inches; 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches^ 

Per  cent 
of  core 

OI 

rods 

« 

y* 

H 

1H 

26 

22        4/0      2Ys, 

1 

10 

409    420    432 

446 

461 

12 

415 

428    442 

459 

477 

14 

'408 

421 

436 

453 

472 

16 

412 

427 

444 

463 

18 

417 

433 

452 

473 

7/0 

IH 

2 

10 

584 

598 

613 

12 

594 

611 

629 

14 

'588 

605 

624 

16 

596 

615 

18 

585  !   604 

625 

27 

23 

4/0 

2K 

1           10 

445    455 

467 

481 

496 

12 

450 

463 

478 

494 

513 

14 

444 

456 

471 

488 

507 

16 

448 

462 

479 

498 

520 

18 

452 

468    487    509 

7/0 

1% 

2          10 

647 

663 

12 

'644 

660 

679 

14 

037    654 

673 

16 

* 

645  !   665 

686 

18 

653  !   675 

28       24 

4/0 

2 

1           10 

492    504 

518 

533 

12 

487    500    515 

531 

550 

14 

493    508    525 

544 

566 

16 

'485 

499    516    535 

557 

18 

489 

505  |   524    546 

570 

7/0 

IK 

2 

10 

699 

714 

12 

i        696 

712 

14 

706 

725  1   747 

16 

697    716 

738  1 

18 

705    727 

751  ! 

29       25        5/0 

2>£ 

1           10 

531    543 

557    572 

1  1 

12 

526 

539    553 

570    588 

14 

532 

546  !   563 

583 

604 

16 

523 

538 

554 

574 

596 

620 

18 

527 

543 

562 

584 

609 

20 

531 

549 

570    595 

7/0 

IK 

2 

10 





753 

768 

12 

766 

784 

14 

'760 

779 

801 

16 

770 

792 

817 

18 

759    781 

805 

20 

767    791 

30       26 

5/0 

2%      1 

12 

....  I   566 

579    593 

010 

628 

14 

572 

586 

603 

023 

644 

16 

578 

594 

614 

636 

660 

18 

'567 

583 

602 

624 

649 

20 

571 

589    610 

635 

662 

7/0 

IK 

1.93 

12 

807 

825 

14 

1  .... 

'800 

820 

841 

16 

!  .... 

811 

833 

857 

18 

799 

821 

846 

20 

807 

832 

859 

146 


TABLE  39 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


(n-l)p]+2fsp'A 
fg=20,000 
,_       /   length  \ 
Max-  (diameter)  =K 


mixture 


n  =  12 
fc=60 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

• 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 

of  core 

i 
« 

H 

H     1 

IK 

Ifc 

31 

27 

5/0 
7/0 

2M 

1M 

1 
1.86 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

eis 

617 

6i3 

619 
625 
631 
637 

620 
628 
636 
644 
652 
660 

635 

645 
656 
666 
676 
687 

651 

664 
678 
691 
704 
717 

848 
861 
875 
888 
901 
914 

670 
686 
702 
718 

867 
883 
899 
915 

842 
853 
863 
873 
884 

'841 
849 
857 

32 

28 

5/0 
7/0 

2 

IX 

1 
1.80 

12 
14 
16 
18 
20 
22 

12 
'  14 
16 
18 
20 
22 

660 

657 
662 
668 
674 
680 

663 
671 
679 
687 
695 
703 

678 
688 
699 
709 
719 
730 

'885 
896 
906 
916 
927 

695 
708 
721 
734 
747 
760 

892 
905 
918 
931 
944 
957 

713 
729 
745 

762 
778 

910 
926 
942 
959 
975 

::: 

"892 
900 

33 

29 

. 

6/0 

7/0 

2M 

IX 

1.73 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 
24 

12 
14 
16 
18 
20 
22 
24 

705 

"707 
713 
719 
725 

708 
716 
724 
732 
740 
748 

723 
733 
743 
754 
764 
775 

739 
752 
765 
778 
792 
805 

932 
945 
958 
971 
985 
998 

758 
774 
790 
806 
822 

951 

967 
983 
999 
1015 

1  .  • 

936 
947 
957 
967 

i  ;;;;  ;;;; 

'934 
941 

34 

30 

6/0 

7/0 

*K 
IX 

1 
1.67 

.... 

755 

754 

759 
765 
771 
777 

755 
762 
770 
778 
786 
794 
802 

769 
779 
790 
800 
811 
821 
831 

786 
799 
812 
825 
838 
851 
864 

975 

988 
1001 
1014 
1028 
1041 
1054 

804 
820 
836 
853 
869 
885 

994 
1010 
1026 
1042 
1058 
1075 

'.'.'.'. 

'976 
984 
992 

979 
990 
1000 
1010 
1021 

147 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


.^  Column  size    ^ 


%  mixture 
12 
600 


Max. 


-l)p]+2ftp'A 
f  ,=20,  000 
I  length  \ 


\diameter 


15 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
~f 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
\\  .  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

.rods 

H 

X 

V* 

1 

1H 

IK 

35 

31       6/0 

2H 

1 

14 

1  • 

810 

827 

847 

868 

16 

818 

838 

860 

884 

18 

'807 

826 

848 

873 

901 

20 

813 

834 

858 

886 

917 

22 

819 

842 

869 

899 

933 

24 

825 

850 

879 

912 

949 

7/0 

1H 

1.62        14 

1034 

1055 

16 

1625 

1047 

1072 

• 

18 

1035 

1060 

1088 

20 

1046 

1073 

1104 

22 

i029 

1056 

1086 

1120 

24 

1037 

1066 

1099 

1136 

36 

32 

6/0 

2 

1 

1    : 
14 

860    877 

896 

918 

16 

868    887 

909 

934 

18 

876    898 

922 

950 

20 

'863 

884    908 

935 

966 

22 

868 

892  j   918 

949 

982 

24 

874 

899  i  929 

962 

999 

7/0 

1H 

1.57. 

14 

1079 

1101 

16 

io7o 

1092 

1117 

18 

i  .  .  .  . 

1081 

1106 

1133 

20 

1091 

1119 

1149 

22 

i675 

1102 

1132 

1166 

24    i  

1083  :  1112 

1145 

1182 

37 

33 

7/0 

2H      1 

14     

:    928 

947 

969 

16   !  

919    938 

960 

985 

18 

927    949 

973 

1001 

20 

914 

935    959 

987 

1017 

22 

919 

943    969 

1000 

1033 

24 

925 

951    980 

1013 

1050 

26 

931 

958  |  990 

1026 

1066 

7/0 

1H 

1.52        14 

1125 

1146 

16 

1138 

1163 

18 

1126 

1151 

1179 

20 

1137 

1164 

1195 

22 

ii20 

1147 

1177 

1211 

24     ... 

1128 

1157 

1190 

1227 

1 

26    1  .... 

1136 

1168 

1204 

1243 

38 

34       7/0 

2H 

1 

14 

980 

1000 

1021 

16 

971    991 

1013 

1037 

18 

' 

979   1001 

1026 

1054 

20 

987  j  1012 

1039 

1070 

22     ... 

972 

995 

1022 

1052 

1086 

24 

978 

1003 

1032 

1065 

1102 

26 

984 

1011 

1013 

1078 

1118 

7/0 

IH 

1.48 

14 

1174 

1196 

16 

1187 

1212 

18 

ii"6 

1200 

1228 

20 

1186 

1214 

1244 

22 

1196 

1227 

12G1 

24 

ii78 

1207 

1240 

1277 

26 

1186 

1217 

1253 

1293 

148 


TABLE  39 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 

n-l)p]+2fep'A 
fs=20,000 
length  \      ,_ 
- 


mixture 


fc=600 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

H 

X 

% 

1 

IH 

IK 

39 

35 

7/0 
7/0 

2H 
1>* 

1 
1.43 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

i026 
1034 
1041 
1049 
1057 
1065 

1035 
1045 
1055 
1066 
1076 
1087 
1097 

1054 
1067 
1080 
1093 
1106 
1120 
1133 

1219 
1232 
1245 
1258 
1271 
1284 
1298 

1075 
1092 
1108 
1124 
1140 
1156 
1173 

1240 
1257 
1273 
1289 
1305 
1321 
1338 

1626 
1032 
1038 

.  .  .  .* 

1220 
1231 
1241 
1251 
1262 

i222 
1230 

40 

36 

7/0 
7/0 

2 

IH 

1 
1.40 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

.... 

1101 
1111 
1122 
1132 
1142 
1153 
1163 

1123 
1136 
1149 
1162 
1175 
1188 
1202 

1286 
1299 
1312 
1325 
1338 
1352 
1365 

1147 
1164 
1180 
1196 
1212 
1228 
1245 

1311 
1327 
1343 
1359 
1375 
1392 
1408 

— 

i094 
1100 

1097 
1105 
1113 
1121 
1129 



i284 
1295 
1305 
1316 
1326 

1276 
1284 
1292 

41 

37 

7/0 
7/0 

2 

m 

1 
1.36 

16 
18 
20 
22 
24 
26 
28 

16 
18 

II 
11 

28 

ii47 
1155 
1163 
1170 
1178 
1186 

1158 
1169 
1179 
1189 
1200 
1210 
1220 

1180 
1193 
1206 
1220 
1233 
1246 
1259 

1334 
1347 
1360 
1373 
1386 
1399 
1413 

1205 
1221 
1237 
1253 
1270 
1286 
1302 

1359 
1375 
1391 
1407 
1423 
1440 
1456 

.... 

ii4o 

1151 
1157 

1333 
1343 
1353 
1364 
1374 

i.332 
1340 

149 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE 

REQUIREMENTS 


Column  size 


1:4%  mixture 
n  =  12 
fc=600 


f,  =  20,000 

Max(tewth\15 

\diameter) 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
f\f 

column 
(inches) 

of  core 

(inches) 

Size  No. 
(A.  S.  & 
W.  Co-.) 

Pitch 

(inches) 

Per  cent 
of  core 

OI 

rods 

:  % 

K 

H 

1 

1H 

IK 

42       38        7/0 

2 

1 

16 

1217 

1239 

1264 

18 

1227 

1252 

1280 

20 

1213 

1238 

1265 

1296 

22 

1221 

1248 

1278 

1312 

24 

1229 

1259 

1292 

1328 

26 

i2ib 

1237 

1269 

1305 

1345 

28 

1216 

1245 

1279 

1318 

1361 

30 

1222 

1253 

1290 

1331 

1377 

'  7/0 

IK 

1.32        16 

1362 

1384 

1409 

18 

1372 

1397 

1425 

20 

1358 

1383 

1410 

1441 

1 

22 

1366 

1393 

1423 

1457 

•  i 

24 

1374 

1403 

1436 

1473 

26 

1382 

1414 

1450 

1490 

28 

isei 

1390 

1424 

1463 

1506 

30 

1366 

1398 

1435 

1476 

1522 

43       39        7/0      l7^ 

1           16 

1278 

1300 

1324 

18 

1288 

1313 

1340 

20 

. 

1274 

1298 

1326 

1357 

22 

1282 

1309 

1339 

1373 

24 

1290 

1319 

1352 

1389 

26 

1298 

1329 

1365 

1405 

28 

1276 

1306 

1340 

1378 

1421 

30 

1282 

1314 

1350 

1391 

1438 

7/0       V/4      1.29        1T> 

1438 

1463 

18 

1451 

1479 

20 

1437 

1464 

1495 

22 

1447 

1477 

1511 

24 

1457 

1490 

1527 

26 

i436 

1468 

1504 

1543 

28 

1444 

1478 

1517 

1560 

30 

— 

1452 

1489 

1530 

1576 

44       40        7/0      1J8'      1           16 

1340 

1362 

1386 

18 

1350 

1375 

1402 

1 

20 

1360 

1388 

1419 

22 

1344 

1371 

1401 

1435 

24 

1352 

1381 

1414 

1451 

26 

1360 

1391 

1427 

1467 

28 

1338 

1368 

1402 

1440 

1483 

30 

1344 

1376 

1412 

1453 

1499 

7/0      1>£      1-25        16 

1487 

1511 

1 

18 

1500 

1528 

20 

i  .... 

'.  '.  '. 

i486 

1513 

1544 

22 

1496 

1526 

1560 

24 

1506 

1539 

1576 

26 

1517 

1553 

1593 

28 

1493 

1527 

1566 

1609 

30 

1501   1538   1579   1625 

150 


TABLE  40 


COLUMNS 


Column  size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


/    length  \ 

MaxA-T^ —       —I  =12 

\diameter 


1:2:4  mixture 
n  =  15 
fc=500 


Size 
of 

column 
(inches) 

Spirals 

Size  of  vertical  round  rods 

eter 
of  core    Size  No. 
(inches)    (A.  S.  & 
W.  Co.) 

!     « 

Pitch 
(inches 

of 
Per  cent     rods 
of  core 

H 

% 

K 

1 

ix  iy* 

15       12       9        IK 

0.5        8 
10 

88 
93 

97 
104 

16       13       8        Hi      0.5        8 
10 

99 
104 

108 
115 

119 

17 

14        7 
0 

\X 

IX 

0.5       •  8 
10 
12 

1.5        8 
10 

I     12 

112 
117 
122 

147 
154 
161 

121 
128 
135 

159 

168 
178 

131 
141 

173 

186 

1 

•  - 

18 

15        6 
2/0 

IX 
IX 

0.5        8 
10 
12 

1.5        8 
10 
12 

125 
130 
136 

'i72 
178 

134 
142 
149 

177 
186 
196 

145 
155 

191 
204 

157 
207 

19 

16        G 
3/0 

\H 

ix 

0.5        8 
10 
12 
14 

1.5        8 
10 
12 
14 

140 
145 
150 
155 

igi 

197 
204 

149 
156 
164 
171 

196 
205 
215 
225 

159 
169 
179 

210 
223 
236 

172 
185 

226 
243 

185 

244 

' 

20 

17        5 
3/0 

IX 
IX 

0.5         8 
10 

If 

1.5        8 
10 
12 
14 

155 
160 
165 
170 

"2is 

224 

164 
171 
179 
186 

216 
226 
235 
245 

175 
185 
195 
205 

230 
243 
256 
269 

187 
200 

246 
263 

201 
264 

21 

18        4 
3/0 

i?i 

'  '  '. 

IX 

0.5         8 
10 
12 
14 

1.5         8 
10 
12 
14 

172 
177 

182 
187 

180 
188 
195 
203 

191 
201 
211 
221 

251 

265 
278 
291 

203 
216 
230 

268 
285 
302 

217    233 
234 

286    306 
307 

246 

"247 
257 
266 

151 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


TABLE  40 


.   Column  size    yi 


1:2:4  mixture 
n  =  15 
fc=500 


=  Afc(l+2.5np' 


12 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
f 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

ot 
rods 

y& 

H 

+ 

H 

1 

IK 

IK 

22 

19 

4 

IH 

0.5 

8 

189 

198 

208 

221 

234 

250 

10 

194 

205 

218 

234 

251 

12 

199 

213 

228 

247 

14 

204 

220 

238 

260 

16 

!   209 

227 

248 

4/0 

IH 

1.5 

8 

i  274 

290 

308 

329 

10 

270   287 

307 

330 

12 

280 

301    325 

14 

268 

289 

314    342 

16 

275 

299 

327  i 

2.3       20 

3 

1M       0.5 

8 

207 

216 

226 

239 

253 

268 

j               ,                  : 

10 

212 

223 

236 

252 

269 

289 

12 

217 

231 

246 

265 

277 

14 

222 

238 

257 

278 

16 

227 

245 

267 

291 

5/0 

1% 

1.5 

8 

298 

314 

332 

353 

10 

311 

331 

354 

379 

12 

'SOS 

324 

349 

376 

14 

313 

337 

366 

i 

16 

'299 

323 

351 

383 

24 

21 

3 

iH 

0.5 

10 

231 

242 

256 

271 

288 

308 

12 

236 

250 

266 

284 

305 

14 

241 

257 

276 

297 

16 

I   246 

264 

286    310 

5/0 

IH 

1.5 

10 

336 

357 

379 

405 

1 

12 

'329 

350 

374 

401 

14 

338 

363 

391 

I    16 

348 

376 

408 

25       22 

2 

IK 

0.5        10 

251 

262 

276 

291 

308 

328 

12 

256 

270 

286 

304 

325 

348 

II    14 

261 

277 

296 

317 

341 

16 

267 

284 

306 

330 

18 

272 

292 

316 

343 

0/0 

2 

1.5       10 

363 

383 

406 

431 

12 

376 

400 

427 

458 

14 

'365 

369 

417 

449 

16 

374 

402 

435 

!         ||    18 

384 

416 

452 

26 

23 

2 

Ui 

0.5        10 

272 

283 

297 

312 

329 

349 

12 

277 

291 

307 

325 

346 

369 

14 

283 

298 

317 

338 

362 

16 

288 

305 

327 

351 

379 

18 

293 

313 

337 

364 

6/0 

1% 

1.5 

10 



411 

433 

459 

12 

'464 

428 

455 

486 

14 

417 

445 

477 

16 

'462 

430 

462 

499 

! 

18 

411 

443 

479 

152 


TABLE  40 


COLUMNS 


Column  Size    <. 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


I  length  \ 
A-r.  —       —  )  =12 
\diameterj 


1:2:4  mixture 
n  =  15 
fe=500 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

H 

H 

H 

1 

IX 

IH 

27 

24 

7/0 

2 
2 

0.5 
1.5 

10 
12 
14 
16 
18 

10 
12 
14 
16 

18 

294 
299 
304 
310 
315 

305 
313 
320 
327 
335 

318 
329 
339 
349 
359 

'432 
446 
459 
472 

334 
347 
360 
373 
386 

439 
457 
474 
491 
508 

351 

368 
384 
401 
417 

462 
484 
506 
527 
549 

370 
391 
411 

487 
514 
541 

431 

440 

28 

25 

1 
7/0 

2 

2 

0.5 
1.5 

10 
12 
14 
16 
18 
20 

10 
12 
14 
16 
18 
20 

317 
322 
327 
332 
337 
343 

328 
335 
343 
350 
358 
365 

341 
351 
361 
371 
381 
391 

'476 
489 
502 
515 

357 
370 
383 
396 
409 
422 

469 
487 
504 
521 
538 
555 

374 
391 
407 
424 
440 

492 
514 
536 
558 
579 

393 
414 
434 
455 

518 
545 
571 
598 

470 
480 

29 

26 

0 
7/0 

2K 

m 

0.5 
1.5 

12 
14 
16 
18 
20 

12 
14 
16 

18 
20 

346 
351 
356 
361 
366 

359 
366 
374 
381 
389 

502 
512 

375 
385 
395 
405 
415 

'507 
520 
533 
546 

393 
407 
420 
433 
446 

518 
536 
552 
570 

588 

414 
431 
447 
464 
481 

545 
567 
589 
610 
632 

438 
458 
478 

576 

602 
630 

30 

27 

0 
7/0 

2X 

IH 

0.5 
1.5 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

371 
376 
381 
386 
391 
396 

384 
391 
399 
406 
413 
421 

400 
410 
420 
430 
440 
450 

418 
431 
445 
457 
471 
484 

550 

568 
585 
602 
620 
636 

439 
456 
472 
489 
505 
522 

578 
600 
622 
643 
664 
686 

462 
483 
503 
524 

608 
635 
662 
689 

'552 
566 
579 
592 

544 
554 

153 


COLUMNS 


TABLE  40 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


Column  siz 


1:2:4  mixture 

n=15 

fc=500 


,_       /    length  \ 
Max.     T  -  —  )  =12 

\diameter 


Spirals                           Size  of  vertical  round  rods 

Size 
of 

Diam-  '                             -vr   » 



eter   1                            Number 

column 

of  core    Size  No.    p-  h    P     t       H 

(inches) 

(inches)    $-S.&   (inches)    oTcor"              H     %     ^     l 

1M 

1>4 

I 

i 

31 

28        2/0      2?^       0.5        12    '396 

410 

425 

444 

465    488 

14 

401 

417 

435 

457    481  i   508 

16 

407 

424 

445 

470    498    529 

18 

312 

432 

455 

483    514 

549 

20 

417 

439 

466 

496    531 

569 

22      422 

447 

476 

509 

548 

7/0      ]»£       1.5        12 

584 

612 

642 

14     

602 

633 

669 

i                               16 

'586 

619 

655 

696 

18 

600 

646 

677 

722 

20     

613 

653 

698 

749 

22     ....  |   588 

626 

670 

720 

32       29        2/0      2*4       0.5        12      423 

436 

452 

471 

491 

514 

14      428 

444 

462 

484 

508 

535 

16      433 

451 

472 

497 

524 

556 

18      438 

458 

482 

509    541 

576 

20      443 

466 

492 

523 

557 

596 

22      448    473    502 

536 

574 

7/0      \%      1.5       12 

646 

677 

||                               14     

637 

668 

704 

16    !  

654 

690 

731 

18 

'635 

670 

712 

758 

20 

648 

688 

734 

784 

22     .... 

661 

705 

755 

33       30        2/0      2^       0.5        12      450 

464 

479 

498 

519 

542 

14 

456 

471 

490 

511 

537 

563 

16 

461 

479 

500 

524 

552 

583 

18 

466 

486 

510 

537 

568 

603 

20 

471 

493 

520 

550 

585 

624 

22 

476 

500 

530 

563 

602 

644 

24 

481 

508 

540 

576 

618 

7/0      1£6       1-5        12 

672 

713 

14     

'672 

704 

740 

16 

690 

726 

767 

18     

670 

707 

748 

794 

20 

684 

724 

770 

821 

22     .... 

697 

741 

791 

847 

24    i  

'668 

710 

758 

813 

34       31        3/0      2^       0.5        14   ||   484 

500 

518 

540 

564 

591 

16    !  489 

507 

528 

552 

581 

611 

18      494 

514 

538 

566 

597 

632 

20 

499 

522 

548 

579 

613 

652 

;                         22 

504 

529 

558 

592 

630 

672 

24 

510    536 

568 

605 

(346 

693 

:    7/0      l$i      1.5       14 

710 

742 

778 

|                               16 

727 

764 

805 

18 

'708 

744 

785 

832 

20 

722 

762 

807 

858 

22 

734 

779 

829 

885 

24 

748 

796 

851 

912 

154 


TABLE  40 


COLUMNS 


Column  size     ^ 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


Afe(l+2.5np')(l  +  (n- 
/  length  \  = 


Max. 


\diameter 


12 


1:2:4  mixture 
n  =  15 
fc  =  500 


Spirals                          Size  of  vertical  round  rods 

Size 

Diam-  :                            I  %»__i 

of 

eter 

rxumuer 

^r 

column 
(inches) 

of  core 

(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

rods 

X 

H 

X 

1 

IK 

IK 

35 

32        3/0      2K       0.5        14 

513 

529 

547 

569 

593 

620 

16 

518 

536 

557 

582 

610 

641 

18 

524 

544 

567 

595 

626 

661 

20 

529 

551 

577 

608 

642 

681 

22 

534 

558 

587 

621 

659 

702 

24 

539 

566 

597 

634 

676 

722 

7/0 

iX 

1.5 

14 

780 

816 

16 

'766 

802 

843 

18 

782 

824 

870 

20 

800 

846 

896 

22 

'773 

818 

867 

924 

24 

786 

834 

889 

950 

36       33        3/0      2^      0.5        14      544 

559 

578 

599 

623 

650 

16      549 

566 

588 

612 

640 

671 

18    ,   554 

574 

598 

625 

656 

691 

20 

559 

581 

608  |  638 

673 

712 

22 

564 

589 

618  !  651 

690 

732 

24 

569 

596 

628  1   664 

706 

752 

26 

574 

603 

638    677 

723 

772 

7/0 

IK 

1.5 

14 



820 

856 

16 

842 

883 

18 

823 

864 

910 

20 

840 

886 

936 

22     .   . 

sis 

857 

907 

963 

, 

24   

826    874 

929 

990 

: 

26 

839    892 

951 

1017 

37       34        3/0      2H 

0.5 

14 

591 

609    630 

655 

682 

16 

580 

598 

619    644 

671 

702 

18 

585 

605 

629 

657 

688 

723 

20 

590 

613  !  639 

669 

704 

743 

22 

595 

620    649    683 

721 

763 

24      600 

627    659    696 

737 

784 

26 

606 

635    669    709 

754 

804 

7/0 

IX 

1.48 

14 

857 

893 

16 

879 

920 

18 

860 

901 

946 

20 

876 

922 

973 

22 

894 

944 

1000 

24 

863   911  |  966 

1027 

26     .... 

876   928  I  988 

1053 

38       35       3/0      2H      0.5 

14 

623 

641    663 

687 

714 

16    1   612 

630 

651    676 

703 

734 

18      617 

638 

661    689 

720 

755 

20      622 

645 

671    702 

737 

775 

22      628 

652 

681  1  715 

753 

795 

24      633 

660 

691    728 

769 

816 

26 

638 

667 

701  !  741 

786 

836 

7/0 

IK 

1.43 

14 

•  1  • 

890 

925 

16 

911 

951 

18 

892 

932 

977 

20 

909 

954 

1003 

22 

926 

975 

1031 

24 

895    943 

996 

1057 

26   ,   .... 

908    959 

1018 

1082 

155 


COLUMNS 


TABLE  40 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


Column  Size 


1:2:4  mixture 

n=75 

fc=500 


/  length  \ 
\diameterj 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

*A 

H 

14 

1 

IK 

iy* 

39 

36 

4/0      2% 

0.5 

16 

663 

684 

709 

735    768 

18 

'65i 

671 

694 

722 

753 

788 

20 

656 

678 

704 

735 

769    808 

22 

661 

685 

714 

748 

786 

829 

24 

666 

693 

724 

761 

803 

849 

26 

!   671 

700 

734 

774 

819 

870 

28      676 

707 

744 

787 

836 

890 

7/0 

m 

1.40 

16 

943 

985 

18   '  .  ..  . 

966 

1012 

20 

943 

987 

1037 

22 

959 

1008 

1063 

24   ||  . 

930 

976 

1030 

1089 

26 

.... 

942 

993 

1051 

1116 

28 

955 

1010 

1072 

1142 

40 

37 

4/0 

2*A 

0.5 

16 

697 

718 

743 

771 

802 

18 

'685 

705 

728 

756 

787 

822 

20      690 

712 

738 

769 

803 

842 

22      695 

719 

748 

782 

820 

863 

24      700 

727 

758 

795 

837    884 

26  .     705 

734 

768 

808 

854    905 

28      710 

741 

778 

821 

869    925 

7/0 

1M 

1.36  !     16     

980   1019 

18 

1001 

1045 

j    20     

'978 

1022 

1071 

22 

994 

1043 

1097 

24     

1011 

1064 

1123 

26 

'976 

1027 

1085 

1148 

I 

28 

989 

1044 

1105 

1174 

41 

38        4/0      2H       0.5        16 

732    753 

778 

806 

836 

18     

740   763 

791 

822 

857 

20      725 

747 

773 

804 

839 

877 

22      730 

754 

783 

817 

856 

898 

24      735 

762 

793 

830 

873 

919 

26      740 

769 

803 

843 

889 

939 

28      745 

776 

813 

856 

906 

960 

30      750 

784 

823 

870 

922 

980 

7/0 

iy2     1.32 

16 

1015 

1054 

18    

1035 

1079 

20     .... 

i6l2 

1057 

1105 

22     

1029 

1077 

1131 

24 

1045 

1098 

1157 

26    

ioi2 

1062 

1118 

1183 

28 

1024 

1078 

1140 

1209 

30 

1037   1095 

1101 

1234 

156 


TABLE  40 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


,_       /  length  \ 
Max.  [-T-.  —       -)  =12 
\dianieteri 


1:2:4  mixture 

n=15 

f c  =  500 


Size 
of 

column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitc-h 
(inches) 

Per  cent 
of  core 

K 

H 

H 

1 

1^ 

IH 

42 

39 

4/0 
7/0 

2H 
1H 

0.5 
1.29 

| 
i 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

'76i 
766 
771 
776 
781 
786 

768 
776 
783 
790 
798 
805 
812 
820 

789 
799 
809 
819 
829 
839 
849 
859 

813 
827 
840 
853 
866 
879 
892 
905 

841 
858 
875 
892 
908 
924 
941 
957 

1052 
1073 
1093 
1114 
1134 
1155 
1175 
1196 

873 
894 
914 
934 
954 
975 
996 
1016 

1091 
1117 
1142 
1167 
1193 
1218 
1244 
1269 

1649 
1065 
1082 
1098 
1115 
1131 

:::: 

1648 
1061 
1074 

43 

40 

4/0 
7/0 

2H 

IK 

0.5 
1.25 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

803 
808 
813 
818 
823 

805 
813 
820 
827 
835 
842 
849 
857 

826 
836 
846 
856 
866 
876 
886 
896 

851 
864 
877 
890 
903 
916 
929 
942 

879 
895 
911 
928 
944 
961 
978 
995 

1087 
1107 
1127 
1147 
1168 
1188 
1208 
1228 

909 
930 
950 
970 
991 
1011 
1032 
1052 

1124 
1150 
1175 
1200 
1225 
1250 
1275 
1300 

i096 
1108 

i085 
1100 
1116 
1133 
1148 
1164 

157 


COLUMNS 


TABLE  41 


mixture 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 

P  =  Afc(l+2.5np'}[l  +  (n- 


Column  Size    * 


12 
600 


\diameterl 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

_r 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

OI 

rods 

H 

H 

H 

1 

1H 

1M 

15       12        9        Us'       0.5 

8      97 

105 

10      101 

112 

10       13        8        IM       0.5         8      110 

118 

10      115 

125 

17 

14        7 

IH       0.5 

8      125 

133 

143 

10      130 

140 

152 

. 

12      134 

146 

0        \H 

1.5         8      157 

168 

180 

10      163 

176 

191 

12 

169 

185 

IS       15        6 

1>£      0-5         8 

141 

149 

158 

170 

! 

10 

145 

155 

168 

! 

12 

150 

162 

2/0 

Ik'       1.5         8 

188 

200 

214 

10 

'l83 

196 

211 

12 

189 

204 

19       16        6        ]?£   j    0.5         8      157 

166 

175 

186 

199 

10 

162 

172 

184 

198 

1  1 

12 

167 

179 

194 

14 

;  171 

186 

3/0 

1% 

l!5 

8 

209 

221 

235 

251 

10 

'264 

217 

233 

250 

12      210 

226 

244 

| 

14    1  216 

234 

20 

17       5 

1>2 

0.5         8      175 

183 

193 

204 

217 

10 

ISO 

190 

202 

216 

12 

185 

197 

211 

14 

189 

204 

221 

1     3/0 

IH 

1.5         8 

231 

244 

258 

274 

10 

240 

255 

273 

12 

233 

248 

267 

| 

14 

239 

257 

278 

21 

18       4 

iH 

0.5 

8 

194 

202 

212 

224 

236 

250 

10 

199 

209 

221 

235 

251 

12 

204 

216 

230 

247 

14 

208 

223 

239 

3/0 

1>2 

1.5 

8 

267 

282 

298 

315 

10 

'264 

279 

297 

317 

12 

272 

290 

312 

14 

'263 

281    302 

158 


TABLE  41 


COLUMNS 


Column  size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


12 


._ 

A/ax. 


/  length  \ 
(-^  —  —  ) 
\diameterl 


1:1%:3  mixture 
n  =  12 
fc=600 


Size 
of 

column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

« 

K 

K 

1 

IH 

IK 

22 

19 

4 
4/0 

1^ 
I* 

0.5 
1.5 

10 
12 
14 
16 

8 
10 
12 
14 
16 

214 
219 
224 
228 
233 

'288 
294 

222 
229 
236 
243 
249 

'289 
297 
306 
314 

232 
241 
250 
259 
269 

293 

304 
316 
327 
339 

243 

255 
267 
279 

307 
322 
337 
352 

256 
271 

323 
342 

270 
341 

23 

20 

3 

5/0 

IK 

IK 

0.5 
1.5 

8 
10 
12 
14 
16 

8 
10 
12 
14 
16 

227 
231 
'  245 
249 
254 

244 
250 
257 
264 
270 

253 
263 
271 
281 
290 

319 
331 
342 
354 
365 

265 
276 
288 
300 
312 

333 

349 
364 
379 
394 

277 
292 
307 

349 
368 
388 

291 
310 

367 
391 

"326 

324 
333 
341 

24 

21        3 
5/0 

1« 
1« 

0.5 
1.5 

10 
12 
14 
16 

10 
12 
14 
16 

262 
267 
272 
276 

272 
279 
286 
293 

'352 
361 
369 

285 
294 
303 
313 

359 
370 
382 
393 

299 
311 
322 
334 

377 

392 
407 
422 

314 
330 

396 
416 

332 
419 

25 

22 

2 
6/0 

IK 

2 

0.5 

1.5 

10 
12 
14 
16 

18 

10 
12 
14 
16 
18 

286 
290 
295 
299 
304 

296 
302 
309 
316 
322 

308 
317 
326 
335 
344 

388 
400 
411 
423 
434 

322 
334 
346 
358 
370 

406 
421 
436 
451 
466 

338 
353 
368 

426 
445 
464 

356 
374 

-448 
472 

1 

390 
398 

407 

26 

23 

2 
6/0 

IK 

IK 

0.5 
1.5 

10 
12 
14 
16 

18 

10 
12 
14 
16 
18 

310 
315 
319 
324 
329 

320 
327 
334 
340 
347 

332 
342 
350 
360 
369 

346 
358 
370 
382 
394 

437 
452 

467 
482 
497 

362 
377 
392 
408 

457 
476 
495 
514 

380 
398 

479 
502 

.'  :  :  : 

'429 
438 

431 

442 
454 
465 

159 


TABLE  41 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


Column  size 


mixture 


=  600 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

H 

H 

H 

1 

1H 

IK 

27 

24 

1 

2 

0.5       10 

335 

346 

358 

372 

388 

405 

12 

340 

352 

367 

384 

403 

424 

14 

345 

359 

376 

396 

418 

443 

16 

849 

366 

385 

408 

433 

18 

354 

372 

394 

420 

448 

7/0 

2 

1.5 

10 

469 

489 

511 

12 

463 

484 

508 

535 

14 

474 

499 

527 

558 

16 

461 

486 

514 

546 

;    18 

470 

497 

529 

565 

28 

25   1 

1 

2 

0.5 

10      362 

372 

384 

399 

414 

432 

12      367 

379 

394 

410 

429 

451 

14 

371 

386 

403 

423 

444 

469 

16 

376 

392 

412 

434 

459 

488 

18 

380 

399 

421 

446 

474 

20 

i  385 

406 

430 

458 

7/0 

2 

1.5       10 

502 

522 

545 

12 

517 

541 

568 

14 

j 

'508 

532 

560 

592 

16     .... 

519 

547 

579 

615 

18 

'503 

531 

562 

598 

20    |  •••• 

512 

542 

577 

29       26 

0 

2M 

0.5 

12      394 

407 

421 

438 

457 

478 

14      399 

413 

430 

450 

472 

497 

16      404 

420 

439 

462 

487 

516 

i        1  1 

18      408 

427 

448 

473 

502 

20      413 

433 

458 

485 

516 

7/0 

1H 

1.5 

12    j  .  .. 

552 

576 

603 

14 

'542 

567 

595 

626 

I  j 

16   li  .  .. 

554 

582 

614 

650 

!  1 

is  :j  .  .. 

'538 

565 

597 

633 

i 

20    !  .  .. 

546 

577 

612 

652 

30 

27        0 

2H 

0.5 

12      423 

435 

450 

467 

486 

507 

14    !  428 

442 

459 

479 

501 

525 

16 

432 

449 

468 

491 

516 

544 

i 

18 

437 

455 

477 

502 

.  531 

563 

1 

20 

442 

462 

486 

514 

546 

22 

446 

469 

495 

526 

561 

7/0 

IK 

1.5 

12 

588 

612 

639 

14   |i  

603 

631 

663 

16 

'596 

618 

650 

686 

18     .... 

602 

633 

669    710 

20 

'583 

613 

648 

688 

22     

591 

624 

664 

707 

160 


TABLE  41 


Column  size  ^ 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


P  =  Afc(l  +2.5np')U  +  (n  - 
I   length  \ 


Max. 


-;-.  —       — 
\diameterj 


12 


1:1)4:3  mixture 
n  =  12 
fc=600 


Size 
'of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

I  Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

% 

\ 

K 

H 

1 

IX 

IK 

31 

1 
28 

2/0 
7/0 

2H 
IK 

0.5 
1.5 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

453 

458 
462 
467 
471 
476 

465 
472 
479 
485 
492 
499 

480 
489 
498 
507 
516 
525 

497 
508 
520 
532 
544 
556 

626 
641 
656 
671 
686 
701 

515 

530 
546 
561 
576 
591 

650 
669 
688 
707 
726 
745 

545 
555 
574 
593 
611 

687 
700 
724 
747 
771 

628 
639 
651 
662 



'629 

32 

29 

2/0 
7/0 

2H 

IM 

0.5 
1.5 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

484 
488 
493 
498 
502 
507 

496 
503 
509 
516 
523 
530 

510 
520 
529 
538 
546 
556 

527 
539 
551 
563 
575 
587 

547 
562 
577 
592 
606 
622 

689 
708 
727 
746 
765 
784 

568 
586 
605 
624 
642 

716 
739 
763 
786 
810 

680 
695 
710 
725 
740 

678 
690 
701 

33 

30 

2/0 

7/0 

2K 

i* 

0.5 
1.5 

12 
14 
16 
18 
20 
22 
24 

12 
14 
16 
18 
20 
22 
24 

516 
520 
525 
530 
534 
539 
544 

528 
535 
541 
548 
555 
562 
568 

542 
552 
561 
570 
579 
588 
597 

559 
571 
583 
595 
607 
619 
631 

578 
593 
608 
624 
639 
654 
669 

729 
748 
767 
786 
805 
824 
843 

599 
618 
637 
656 
674 
693 

756 
779 
803 
826 
850 
873 

720 
735 
750 
765 
780 
795 

.... 

.... 

719 
730 
742 
753 

716 

34 

31 

3/0 

7/0 

2H 

l)i 

0.5 
1.5 

14 
16 
18 
20 
22 
24 

.14 
16 
18 
20 
22 
24 

553 
558 
563 
567 
572 
577 

568 
574 
581 
588 
595 
602 

585 
594 
603 
612 
622 
631 

605 
617 
629 
641 
653 
665 

762 
777 
792 
807 
822 
837 

627 
642 
657 
672 
687 
702 

790 

809 
828 
847 
866 
885 

651 
670 
688 
707 
726 
745 

821 

845 
868 
892 
915 
939 



'7ei 

772 
784 
795 

••••  (  '••• 

11 


161 


COLUMNS 


TABLE  41 


1:1^4:3  mixture 
n  =  12 
fc  =  600 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 

P=Afc(l+2.5np' 
Max. 


,  Column  si. 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

% 

H 

% 

1 

IH 

IK 

35 

32 

3/0 
7/0 

2H 
IK 

0.5 
1.5 

14 
16 
18 
20 
22 
24 

14 
16 
18 
20 
22 
24 

587 
592 
597 
601 
606 
611 

602 
608 
615 
622 
629 
635 

619 

628 
637 
646 
655 
664 

638 
650 
662 
674 
686 
698 

661 
676 
691 
706 
721 
736 

833 

852 
871 
890 
909 
928 

685 
704 
722 
741 
760 
779 

864 
888 
911 
935 
958 
982 

'826 
838 

820 
835 
850 
865 
880 

36 

33 

3/0 

7/0 

2M 

IX 

0.5 
1.5 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

623 
627 
632 
637 
641 
646 
652 

637 
644 
650 
657 
664 
670 
677 

654 
663 
673 
682 
691 
700 
709 

674 
685 
697 
709 
721 
733 
745 

696 
711 
726 
741 
756 
771 
786 

877 
896 
915 
934 
953 
972 
991 

721 
739 
758 
777 
795 
813 
832 

909 
932 
956 
979 
1002 
1026 
1049 

.... 

'87i 

882 
894 

'879 
894 
909 
925 
940 

37 

34 

3/0 
7/0 

2H 

1H 

0.5 
1.48 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

'  '664 
;   668 
673 
678 
682 
687 

673 
680 
687 
693 
700 
707 
714 

690 
699 
708 
717 
727 
736 
745 

710 
722 
734 
746 
758 
770 
782 

732 
747 
76? 
777 
792 
807 
822 

919 
937 
956 
975 
994 
1013 
1031 

757 
775 
794 
813 
831 
850 
868 

949 
973 
996 
1019 
1042 
1065 
1089 

'923 
935 

921 
936 
950 
965 
980 

38 

35 

3/0 
7/0 

2H 
IH 

0.5 
1.43 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

'761 
706 
710 
715 
720 
725 

711 
717 
724 
731 
738 
744 
751 

727 
737 
746 
755 
764 
773 
782 

747 
759 
771 
783 
794 
806 
819 

769 
784 
800 
815 
830 
845 
860 

956 
975 
994 
1013 
1031 
1050 
1069 

794 
813 
832 
851 
869 
887 
906 

987 
1010 
1033 
1056 
1080 
1103 
1126 

'96i 
973 

958 
973 
988 
1003 
1018 

162 


TABLE  41 


COLUMNS 


Column  Size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


P=Afc(l+2.5np')[l  +  (n- 


Max. 


I   length  \ 
{diameter/ 


12 


%: 3  mixture 
12 
600 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  raund  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

H 

H    H    1    iM   1M 

39 

36 

4/0 
7/0 

*M 

iK 

0.5 
1.40 

16 
18- 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

16 
18 
20 
22 
24 
26 
28 

'744 

749 
754 
758 
763 
768 

756 
763 
769 
776 
783 
789 
796 

775 

784 
794 
803 
812 
821 
830 

798 
810 
821 
833 
845 
857 
869 

823 
838 
853 
869 
884 
899 
914 

1016 
1035 
1054 
1073 
1092 
1110 
1129 

851 

870 
889 
908 
926 
945 
964 

1052 
1075 
1098 
1121 
1145 
1168 
1191 

-  •••• 

iois 

1030 
1044 
1059 
1074 

;;;; 

ioos 

1014 
1025 

40 

37 

4/0 
7/0 

2% 

IH 

0.5 
1.36 

"784 
788 
793 
798 
803 
807 

795 
802 
809 
816 
822 
829 
836 

815 
824 
833 
842 
851 
860 
869 

837 
850 
861 
873 
885 
897 
909 

863 
878 
893 
909 
924 
939 
954 

1056 
1074 
1093 
1111 
1130 
1148 
1167 

891 
909 
928 
947 
965 
984 
1003 

1091 
1113 
1136 
1159 
1182 
1205 
1228 

;;  : 

1054 
1065 

1055 
1070 
1084 
1098 
1113 

41 

38 

1 

4/0 
7/0 

*H 

IK 

0.5 
1.32 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

'829 
834 
839 
844 
,  848 
852 

836 
843 
850 
856 
863 
870 
876 
883 

856 
865 
874 
883 
892 
901 
910 
919 

879 
890 
902 
914 
926 
938 
950 
962 

903 
918 
934 
949 
964 
979 
994 
1009 

1096 
1115 
1133 
1152 
1170 
1188 
1207 
1225 

932 
951 
970 
988 
1007 
1025 
1044 
1063 

1131 
1154 
1176 
1199 
1221 
1244 
1267 
1289 

••'• 

i094 
1105 
1116 

16&5 
1109 
1124 
1138 
1153 
1167 

163 


COLUMNS 


TABLE  41 


1:1%:3  mixture 
n  =  12 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


12 


fnlnmrt  size     %. 


Max. 


Size 
of. 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(.inches) 

Per  cent 
of  core 

ys 

H 

7A 

1 

IH 

IK 

42 

39 

4/0 
7/0 

2M 

1}'2 

0.5 
1.29 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

'S71 
876 
880 
885 
889 
894 

878 
885 
891 
898 
905 
911 
918 
924 

897 
906 
916 
925 
934 
943 
953 
962 

920 
932 
944 
956- 
967 
979 
991 
1003 

945 

960 
975 
990 
1004 
1019 
1034 
1050 

1140 
1158 
1176 
1194 
1212 
1230 
1249 
1267 

973 

992 
1010 
1029 
1048 
1066 
1084 
1103 

1172 
1196 
1219 
1241 
1264 
1286 
1309 
1331 

ii37 

1148 
1159 

li38 
1152 
1167 
1181 
1195 
1210 

43 

40 

4/0 
7/0 

2H 
IH 

0.5 
1.25 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

"gis 

923 

928 
932 

1  937 

921 
927 
934 
941 
947 
954 
961 
968 

940 
949 
958 
968 
977 
986 
995 
1004 

962 
974 
986 
998 
1010 
1022 
1034 
1046 

988 
1003 
1018 
1033 
1048 
1062 
1077 
1092 

1181 
1199 
1217 
1235 
1253 
1271 
1289 
1307 

1016 
1035 
1053 
1072 
1090 
1109 
1128 
1146 

1215 
1237 
1259 
1282 
1304 
1326 
1348 
1371 

1179 
1193 
1207 
1222 
1236 
1250 

.... 

ii90 

1200 

164 


TABLE  42 


Column  size 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


1:1:2   mixture 

n=10 

fc=725 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

of 
rods 

H 

H 

H 

1 

IX 

IH 

15 

12 

9 

1H 

0.5 

8 

110 

118 

1 

10 

115 

125 

16 

13 

8 

IH 

0.5 

8 

126 

134 

! 

10 

;  131. 

141 

17 

14 

7 

IK 

0.5 

8 

144 

151- 

161 

10 

148 

158 

170 

12 

153 

164 

0 

IH 

1.5 

8 

175 

185 

197 

10 

181 

193 

207 

12 

186 

201 

18       15      .6 

1H 

0.5 

8      162 

170 

179 

190 

10      167 

177 

188 

12 

171 

183 

2/0 

1H 

1.5 

8 

208 

219 

233 

10 

'264 

216 

230 

12 

209    224 

19 

16 

6 

IH 

0.5 

8 

182 

190 

199 

210 

223 

10 

186 

196 

208 

222 

12 

191 

203 

217 

14 

195 

211 

3/0 

i^ 

1.5 

8 

232 

244 

257 

272 

10 

'228 

240 

254 

271 

12 

233 

248 

265 

14 

239 

257 

20 

17 

5 

1H       0.5 

8 

203 

211 

220 

231 

243 

10 

208 

217 

229 

243 

12 

212 

224 

238 

14 

217 

231 

247 

3/0 

m 

1.5 

8 

258 

269 

283 

298 

10 

266 

280 

296 

12 

'259 

274 

291 

14 

265 

282 

302 

21 

18 

4 

IK 

0.5 

8      225 

234 

243 

254 

266 

280 

10      230 

240 

252 

265 

280 

12 

235 

247 

260 

277 

14 

239 

254 

269 

3/0 

IK 

1.5 

8 

297 

310 

325 

342 

10 

'293 

308 

324 

343 

12 

301 

318 

338 

1 

14 

'292 

310 

329 

165 


COLUMNS 


TABLE  42 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


•Column  size 


1:1:2  mixture 
'ri  =  10 
fc  =  725 


Maxl  lw"L\=12 
\diameter  / 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 

_r 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 

(inches) 

Per  cent 
of  core 

OI 

rods 

*A 

H 

V* 

1 

IH 

IH 

22 

19 

4 

IH 

0.5 

8 

249 

257 

266 

277 

290 

303 

10 

254 

264 

275 

289 

304 

12 

258 

270 

284 

300 

14 

263 

277 

293 

312 

16 

267 

283 

302 

4/0      1% 

1.5         8 

326 

339 

354 

370 

10 

'322 

336 

353 

372 

12 

330 

347 

367 

14 

'321 

338 

358 

381 

16      327 

346 

369 

23 

20        3        IH       0.5         8    i  274 

282 

291 

302 

315 

328 

10    i  279 

289 

300 

314 

329 

346 

12    ;  283 

295 

309 

326 

344 

14 

i  288 

302 

318 

337 

16 

292 

808 

327 

349 

5/0      1% 

1.5         8 

356 

369 

384 

401 

10 

367 

384 

402 

423 

12     

'sei 

378 

398 

420 

14 

369 

389 

412 

1 

i    16      357 

377 

399 

426 

24 

21        3 

1% 

0.5        10 

305 

315 

326 

340 

356 

372 

12 

309 

321 

335 

352 

370 

14   '   314 

328 

344 

363 

16 

319 

334 

353 

375 

5/0      IM 

1.5        10 

399 

416 

435 

455 

12 

393 

410 

430 

452 

14 

401 

421 

444 

16     

409 

432 

458 

25 

22        2        1%       0.5        10      333 

342 

354  1   368 

383 

400 

12      337 

349 

363    379 

398 

418 

:  j 

14      341 

356 

372 

391 

412 

16      346 

362 

381 

402 

18 

350 

368 

389 

414 

6/0 

2 

1.5        10 

433 

449 

468 

490 

12 

444 

463 

486 

511 

14 

'434 

454 

478 

504 

16 

442 

465 

492 

18 

450 

476 

506 

1 

26 

23 

2 

IH       0.5        10    i   361 

372 

383 

396 

412 

429 

12      366 

378 

392 

408 

427 

447 

14      370 

385 

401 

420 

442 

16      375 

391 

410 

431 

456 

18    1   379 

397 

418 

443 

6/0      1%  '     1.5 

10 

485 

503 

525 

12 

'479 

499 

521 

546 

14 

490 

513 

539 

16 

'478 

501 

527 

557 

18    |;  .... 

485 

512 

541 

. 

lf>6 


TABLE  42 


COLUMNS 


Column  size 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


Max.    --    =12 


n=10 
fc  =  725 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
•(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent  1 
of  core 

*A 

H 

H 

1 

IK 

in 

27 

24 

7/0 

Q 

2 

0.5 
1.5 

10 
12 

146 

18 

10 
12 
14 
16 

18 

392 
396 
401 
305 
410 

401 
408 
415 
421 
428 

413 

422 
431 
440 
449 

'515 
526 
537 
548 

427 
438 
450 
461 
473 

522 
536 
550 
564 

578 

442 
457 
471 
486 
500 

540 
558 
576 
594 
612 

459 

477 
495 

561 
583 
605 

:::.' 

'si  5 

522 

28 

25 

1 
7/0 

2 

0.5 
1.5 

10 
12 
14 
16 
18 
20 

10 
12 
14 
16 
18 
20 

423 
428 
432 
437 
441 
446 

433 
440 
447 
453 
459 
465 

445 
453 
462 
471 
480 
489 

458 
470 
481 
493 
504 
516 

560 
574 
588 
602 
616 
630 

473 
488 
503 
517 
532 

578 
596 
614 
632 
650 

490 
508 
527 
545 

599 
621 
644 
666 

• 

'56i 
569" 

'565 
576 
587 
597 

29 

26 

0 
7/0 

2M 

m 

0.5 
1.5 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

460 
464 
469 
473 
478 

472 
479 
485 
491 
498 

'eoi 

608 

486 
495 
504 
512 
521 

'605 
616 
626 
637 

502 
513 
525 
537 

548 

613 

628 
642 
656 
670 

521 
535 
550 
564 
579 

636 
654 
672 
690 
707 

541 
559 
577 

662 
683 
705 

30 

27 

0 
7/0 

2H 

IH 

0.5 
1.5 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

494 
499 
503 
508 
512 
517 

506 
513 
519 
525 
531 
538 

520 
529 
537 
546 
555 
564 

536 
548 
559 
570 
582 
593 

655 
670 
684 
698 
712 
726 

554 
569 
583 
598 
613 
628 

678 
696 
714 
731 
749 
767 

575 
593 
611 
629 

703 
725 
747 
769 

"650 
658 

'657 
668 
679 
689 

167 


COLUMNS 


1:1:2  mixture 

n=10 

f c=7  25 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 

P=Afc(l+2.5np'j[l+(n-l)p] 
Max.  t--    =12 


TABLE  42 


i^  Co/if 777/7  size    y. 


Spirals 

Size  of  vertical  round  rods 

Size 
of 

Diam- 
eter 

Number 
_* 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  &. 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

OI 

rods 

H 

H 

% 

1 

IK 

IX 

31 

28 

2/0 

2% 

0.5 

12 

530 

541 

555 

571 

590 

610 

14 

534 

548 

564 

583 

605 

628 

16 

539 

554 

573 

595 

619 

647 

18 

543 

560 

582 

606 

633 

665 

20 

548 

567 

590 

618 

648 

682 

22 

552 

573 

599 

629 

663 

7/0 

IK 

1.5 

12 

698 

721 

746 

14 

713 

739 

768 

16 

'766 

727 

757 

790 

18 

711 

741 

775 

812 

20 

722 

755 

792 

834 

22 

'76! 

733 

769 

810 

32 

29 

2/0 

2H 

0.5 

12 

565 

577 

592 

608 

626 

647 

14 

570 

584 

600 

620 

641 

665 

16 

'    574 

590 

609 

631 

655 

683 

18 

579 

597 

618 

642 

670 

701 

20 

583 

603 

627 

654 

685 

718 

22 

588 

610 

636 

666 

699 

7/0      . 

IK 

1.5 

12 

765 

792 

14 

'757 

783 

813 

16 

771 

801 

835 

18 

'756 

785 

819 

857 

20 

767 

800 

837 

879 

22 

777 

814 

855 

33 

30 

2/0 

2H 

0.5 

12 

604 

616 

629 

646 

664 

685 

14 

608 

622 

638 

657 

678 

702 

16 

613 

628 

647 

669 

693 

720 

18 

617 

635 

656 

680 

708 

738 

20 

622 

641 

665 

691 

723 

757 

22 

526 

648 

674 

703 

737 

775 

24 

631 

654 

683 

715 

752 

7/0             IK 

1.5 

12 

812 

836 

14 

'803 

830 

858 

16 

817 

848 

880 

18 

'802 

832 

866 

902 

'  20 

813 

846 

883 

925 

22 

824 

860 

901 

947 

24 

'800 

834 

873 

919 

34 

31 

3/0 

2% 

0.5 

14 

647 

661 

677 

696 

718 

742 

16 

652 

668. 

686 

708 

733 

760 

18 

656 

674 

695 

720 

747 

778 

20 

661 

680 

704 

731 

762 

796 

22 

665 

687 

713 

743 

777 

813 

24 

670 

693 

722 

754 

791 

831 

7/0 

IK 

1.5 

14 

851 

878 

907 

1          16        ! 

865 

895 

•929 

18 

'850 

880 

913 

951 

20 

861 

894 

931 

973 

22 

872 

908 

949 

995 

24 

882 

922 

966 

1017 

168 


TABLE  42 


Column  size     <. 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


P=Afc(l+2.5np')(l  +  (n- 
I   length  \ 

)  =12 


Max' 


diameter 


1:1:2  mixture 

n=10 

fc  =  725 


Size 
of 
column 
(inches) 

Diam- 
eter 
of  core 
(inches) 

j 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.)  ! 

Pitch 
(inches) 

Per  cent 
of  core 

K 

% 

H 

1 

IX 

IH 

35 

32 

3/0 
7/0 

2K 
IK 

0.5 
1.5 

14 
16 
18 
20 
22 
24 

14 
16 
18 
20 
22 
24 

688 
692 
697 
701 
706 
710 

702 
708 
715 
721 
728 
734 

717 

727 
736 
745 
753 
762 

737 

748 
760 
771 
782 
795 

758 
773 
787 
802 
817 
831 

927 
945 
963 
981 
998 
1016 

782 
800 
818 
836 
854 
872 

956 
978 
1000 
1022 
1045 
1067 

915 
929 
943 
957 
972 

.... 



'921 
931 

36 

33 

3/0 

7/0 

2K 

IK 

0.5 
1.5 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

729 
734 
738 
743 
747 
752 
756 

743 
749 
756 
762 
769 
775 
782 

759 
768 
777 
786 
795 
804 
812 

778 
790 
801 
813 
825 
836 
848 

800 
814 
829 
843 
858 
873 
887 

978 
996 
1013 
1031 
1049 
1067 
1086 

824 
842 
860 
878 
896 
914 
932 

1007 
1029 
1051 
1073 
1095 
1117 
1140 

'972 
983 
993 

980 
994 
1008 
1022 
1036 

37 
38 

34 

3/0 

7/0 

99i 

IK 

0.5 
1.48 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

'778 
782 
787 
791 
796 
800 

787 
793 
800 
806 
813 
819 
826 

803 
812 
820 
829 
838 
846 
855 

821 
833 
844 
856 
867 
879 
890 

843 
858 
872 
886 
900 
915 
930 

1027 
1044 
1061 
1079 
1097 
1114 
1132 

867 
885 
903 
920 
938 
956 
975 

1054 
1077 
1099 
1121 
1143 
1165 
1187 

1628 
1042 
1056 
1070 
1084 

•••• 

ioso 

1041 

35 

3/0 

7/0 

2H 
IK 

0.5 
1.43 

14 
16 
18 
20 
22 
24 
26 

14 
16 
18 
20 
22 
24 
26 

"82i 
826 
830 
835 
839 
844 

830 
837 
843 
850 
856 
863 
869 

846 
854 
863 
872 
881 
890 
899 

866 
877 
888 
900 
912 
923 
935 

887 
901 
916 
930 
945 
960 
975 

1072 
1089 
1107 
1125 
1142 
1160 
1178 

911 
929 
947 
965 
983 
1000 
1018 

1100 
1122 
1144 
1166 
1188 
1209 
1231 

1673 
1087, 
1101 
1115 
1129 

:::: 

| 

i075 
1086 

169 


COLUMNS 


TABLE  42 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


Column  size    .^i 


P 


1:1:2  mixture 
n  =  10 


Afe(l+2.5np')[l+(n-l)p] 


Spirals 

Size  of  vertical  round  rods 

Size 

Diam- 

t 

of 

eter 

JN  umber 

of 

column 
(inches) 

of  core 
(inches) 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent 
of  core 

j 

OI 

rods 

H 

! 

2i 

H 

1 

IH 

IX 

39 

36 

4/0 

2H 

0.5 

16 

866 

882 

901 

922 

947 

974 

I    18 

871 

888 

910 

934 

961 

992 

20 

875 

895 

919 

945 

976 

1010 

22 

880 

901 

928 

957 

991 

1028 

24 

884 

908 

936 

969 

1005 

1046 

26 

889 

914 

945 

980 

1020 

1064 

28 

893 

920 

954 

992 

1034 

1082 

7/0    iy2 

1.40 

16 

1133 

1167 

18 

1151 

1188 

20 

ii32 

1168 

1210 

22 

1146 

1186 

1232 

24 

ii2i 

1159 

1204 

1254 

26 

1131 

1173 

1221 

1275 

28 

1141 

1187 

1239 

1297 

40 

37 

4/0 

2H 

0.5        16 

929 

948 

968 

993 

1021 

18 

'6i8 

935 

956 

980 

1008 

1039 

20 

922 

942 

965 

991 

1023 

1057 

22 

927 

948 

974 

1003 

1037 

1075 

24 

931 

955 

983 

1015 

1052 

1093 

26 

936 

961 

991 

1026 

1066 

1111 

28 

940 

967 

1000 

1038 

1081 

1129 

7/0 

1>2 

1.36       16 

1183 

1216 

18 

1201 

1237 

20 

1181 

1219 

1259 

22 

1195 

1236 

1280 

24 

1209 

1253 

1302 

26 

iisi 

1223 

1271 

1323 

28   | 

1191 

1237 

1289 

1345 

41 

38 

4/0 

2^       0.5        16 

978 

996 

1017 

1041 

1069 

18 

984 

1005 

1029 

1056 

1087 

20 

97i 

991 

1013 

1040 

1071 

1105 

22 

976 

997 

1022 

1052 

1086 

1123 

24 

980 

1004 

1031 

1063 

1100 

1141 

26 

985 

1010 

1040 

1075 

1115 

1159 

1 

28 

989 

1016 

1049 

1086 

1130 

1177 

30 

994 

1022 

1058 

1098 

1144 

1196 

7/0 

ll£ 

1.32 

16 

1232 

1264 

*  7z 

18 

1249 

1285 

20 

1230 

1266 

1306 

22 

1244 

1284 

1328 

24 

1257 

1301 

1350 

26 

1230 

1271 

1318 

1371 

28 

. 

1240 

1285 

1336 

1393 

30 

1251 

1298 

1353 

1415 

170 


TABLE  42 


Column  size 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

CHICAGO  BUILDING  CODE  REQUIREMENTS 


19 

12 


.—f-.  — 
\diameter 


1:1:2  mixture 
n  =  10 
fe=725 


Size 
of 
column 
(inches) 

Diam-  i 
eter 
of  core 
(inches) 

Spirals 

Number 
of 
rods 

Size  of  vertical  round  rods 

Size  No. 
(A.  S.  & 
W.  Co.) 

Pitch 
(inches) 

Per  cent  j 
of  core  ! 

X 

H 

H 

1 

IH 

I« 

42 

39 

4/0 

7/0 

2H 
1H 

0.5 
1.29 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

1620 
1025 
1029 
1034 
1038 
1042 

1027 
1033 
1040 
1046 
1053 
1059 
1065 
1072 

1045 
1054 
1063 
1071 
1080 
1089 
1098 
1107 

1067 
1078 
1090 
1101 
1112 
1124 
1136 
1147 

1091 
1106 
1120 
1135 
1149 
1163 
1178 
1193 

1283 
1300 
1317 
1334 
1351 
1368 
1386 
1403 

1118 
1136 
1154 
1172 
1190 
1208 
1226 
1244 

1315 
1336 
1357 
1378 
1399 
1420 
1441 
1463 

1281 
1294 
1308 
1321 
1335 
1349 

'.'.'.'. 

i 

1280 
1290 
1300 

43 

40 

4/0 
7/0 

2H 
1H 

0.5 

,.„ 

16 
18 
^0 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 
28 
30 

i073 
1078 
1083 
1088 
1092 

1  •  • 

1077 
1083 
1090 
1096 
1103 
1109 
1116 
1122 

1096 
1104 
1113 
1122 
1131 
1140 
1149 
1158 

1117 
1129 
1140 
1152 
1163 
1175 
1186 
1198 

1142 
1156 
1171 
1186 
1200 
1215 
1229 
1244 

1333 
1350 
1367 
1385 
1402 
1419 
1436 
1453 

1169 
1187 
1205 
1223 
1241 
1259 
1277 
1295 

1366 
1387 
1408 
1429 
1450 
1471 
1492 
1513 

1332 
1345 
1359 
1372 
1386 
1400 

i  •  • 

•••• 

1340 
1350 

171 


COLUMNS 


TABLE  43 


71=15 

fc=800 


ROUND  CORED  HOOPED  COLUMNS 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 

LOS  ANGELES  AND  MILWAUKEE  BUILDING 

CODE  REQUIREMENTS 

P=Afc[l+(n-l)p] 


Cotumn  size 


Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

IK 

1M 

H 

H 

| 

H        1 

IK 

134 

H 

H 

H 

1 

10 

7 

6 

*57.0 

*51.4 

*60.5 

11 

8 

6 

*66.4 

*78  .  0  .  . 

60.8 

*69.9 

c 

*7*  2; 

*67.7 

*79.8 

12 

9 

6              77.1 

71.5 

8 
' 

78.4 

13                   10 

6          j     89   0 

83  4 

92.5 

8           j   97.8 

90.3 

14 

11 

6            102  2 

1138 

96.6 

105.7 

116.4 

8           1111.  0  

103.5 

115.6 

10 

110.4 

15 

12                      6 

116.7 

128.3 

111.1 

120.2 

130.9 

8 

125.5 

140.9  

118.0 

130.1 

10 

134  3 

124.9 

140.0 

10 

13                      6 

132.4 

144.0 

157.6 

126.8 

135.9 

146.6 

159.0 

8 

141.2 

156.6  

133.7 

145.8 

160.1 

10 

150.0 

140.6 

155.7 

17 

14                      6 
8 

149.3 
158.1 

160.9  174.5 
173.5  191.7 

190.3  

143.7 
150.6 

152.8 
162.7 

163.5 

177.0 

175.9 

189.9 

10 

166.9 

186.1  i  ,  

157.5  172.6 

190.4 

12 

175.6 

164.3 

182.5 

18 

15                      6 

167.6 

179.2 

192.8 

208.  G!  

162.0171.0 

181.8 

194.2 

.  8 

176.4 

191.8 

210.0 

168.9  181.0 

195.3 

211.8 

10 

185.2 

204.4 

175.8 

190.9 

208.7 

12 

193.9 

217.0 

182.6 

200.8 

19                   10                      8 

195.9 

211.3 

229.5 

250.5  

188.4 

200.5 

214.8 

231.3'250.0 

10 

204.7 

223.9 

246.6 

195.3 

210.4 

228.2 

248.9 

12 

213.4 

236.5 

202.1 

220.3 

241.7 

14 

222.2 

249.1 

209.0 

230.2 

20                   17 

8 

216.6 

232.0 

250.2 

271.2  .. 

209.1 

221.2235.5 

252.0270.7 

10 

225.4 

244.6 

267.3)  

216.0 

231.1  248.9 

269.6, 

12 

234.1 

257.2 

......  1  

222.8 

241.0  262.4 

14 

242.9 

269.8 

229.7 

250.9 

275.9 

I  

21                   18 

8 

238.6 

254.0 

272.2 

293.2'317.0 

243.2 

257.5 

274.0292.7 

313.5 

10 

247.4 

266.6 

289.3 

315.  6j  

238  '.  6 

253.1 

270.9 

291.6314.9 

12 

256.1 

279.2 

306.5 

244.8 

263.0  984  4 

309.2 

14 

264.9 

291.8 

251.7 

272.9 

297.9 

22                   19 

8 

261.8 

277.2 

295.4 

316.4340.2 

266.4 

280.7 

297.2315.9 

336.7 

10 

270.6 

289.8 

312.5 

338.8  ..-.[.I  

26i!2 

276.3 

294.1 

314.8338.1 

12 

279.3 

302.4 

329.7 

1  

268.0 

286.2 

307.6 

332.4 

14 
16 

288.1 
296.8 

315.0 
327.6 

346  8 

274.9 

281.8 

296.1 
306.0 

321.1 
334.6 

350.0 

23 

20 

8 
10 

286.4 
295.2 

301.8320.0341.0364.8 
314.41337.1  363.4393.1 

391.4 

291.0 
300.9 

305.3 
318.7 

321.8340.5361.3 
339.4362.7388.8 

12            303.9 

327.  0354.31  385.  8 



262!  6 

310.8 

332.2 

357.0  385.  Oj 

14            312.7 
16            321.4 

339.6 
352.2 

371.4 
388.6 



299.5 
306.4 

320.7(345.7 
330.6359.2 

374.6 
392.1 

These  columns  contain  more  than  4  %  of  steel. 


172 


TABLE  43 


COLUMNS 


i^  Column  size    ^ 

ROUND  CORED  HOOPED  COLUMNS 
SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
LOS  ANGELES  AND  MILWAUKEE  BUILDING 
CODE  REQUIREMENTS 

=  15 

\                             \ 

1/4^^-?^  ik 

**&& 

—  oUU 

Size 
of 

column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

M 

1 

IK 

IK 

.* 

H 

M 

1 

IK 

IX 

24 
25 

26 
27 
28 

29 
30 

31 
32 
33 

21 
22 

23 
24 
25 

26 
27 

28 
29 
30 

10 
12 
14 
16 

10 
12 
14 
16 

18 

10 
12 
14 
16 

18 

10 

If 

16 

18 

10 
12 
14 
16 
18 
20 

12 
14 
16 
18 
20 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 

12 
14 
16 
18 
20 
22 
24 

320.9 
329.6 
338.4 
347.1 

347.9 
356.6 
365.4 
374.1 
382.9 

340.1 
352.7 
365.3 
377.9 

367.1 
379.7 
392.3 
404.9 
417.5 

395.4 
408.0 
420.6 
433.2 
445.8 

424.9 
437.5 
450.1 
462.7 
475.3 

455.7 
468.3 
480.9 
493  .  5 
506.1 
518.7 

500.3 
512.9 
525.5 
538.1 
550.7 

533.7 

362.8 
380.0 
397.1 
414.3 

389.8 
407.0 
424.1 
441.3 
458.4 

418.1 
435.3 
452.4 
469.6 
486.7 

447.6 
464.8 
481.9 
499.1 
516.2 

478.4 
495.6 
512.7 
529.9 
547.0 
564.2 

527.6 
544.7 
561.9 
579.0 
596.2 

561  .  0 

389.1 
411.5 

418.8 



318.3 

325.2 
332.1 

326.6 
336.5 
346.4 
356.3 

353.6 
363.5 
373.4 
383.3 
393.2 

381.9 
391.8 
401.7 
411.6 
421.5 

42i!3 
431.2 
441.1 
451.0 

344.4 
357.9 
371.4 
384.9 

371.4 
384.9 
398.4 
411.9 
425.3 

399.7 
413.2 
426.7 
440.2 
453.6 

429.2 
442.7 
456.2 
469.7 
483.1 

460.0 
473.5 
487.0 
500.5 
513.9 
527.4 

505.5 
519.0 
532.5 
545.9 
559.4 

538.9 
552.4 
565.9 
579.3 
592.8 
606.3 

573.4 
586.9 
600.4 
613.8 
627.3 
640.8 

609.2 
622.7 
636.2 
649.6 
663.1 
676.6 

646.3 
659.8 
673.3 
686.7 
700.2 
713.7 
727.1 

265.1 
382.7 
400.3 
417.8 

392.1 
409.7 
427.3 
444.8 
462.4 

420.4 
438.0 
455.6 
473.1 
490.7 

449.9 
467.5 
485.1 
502.6 
520.2 

480.7 
498.3 
515.9 
533  .  4 
551.0 
568.6 

530.3 
547.9 
565.4 
583.0 
600.6 

563.7 
581.3 
598.8 
616.4 
634.0 
651.6 

598.2 
615.8 
633.3 
650.9 
668.5 
686.1 

634.0 
651.6 
669.1 
686.7 
704.3 
721.9 

671.1 
688.7 
706.2 
723.8 
741.4 
759.0 
776.6 

388.4 
410.7 

415.4 
437.7 
460.0 

443.7 
466.0 
488.3 
510.5 

473  .  2 
495.5 
517.8 
540.0 
562.3 

504.0 
526.3 
548.6 
570.8 
593.1 

558.3 
580.6 
602.8 
625.1 
647.4 

591.7 
614.0 
636.2 
658.5 
680.8 
703.0 

626.2 
648.5 
670.7 
693.0 
715.3 
737.5 

662.0 
684.3 
706.5 
728.8 
751.1 
773.3 

699.1 
721.4 
743.6 
765.9 
788.2 
810.4 
832.7 

414.5 

441.5 
469.0 

469.8 
497.3 

499.3 
526.8 
554.3 

530.1 
557.6 
585.1 
612.6 

589.6 
617.1 
644.6 

623.0 
650.5 
678.0 
705.5 

657.5 
685.0 
712.5 
740.0 
767.4 

693.3 
720.8 
748.3 
775.8 
803.2 

730.4 
757.9 
785.4 
812.9 
840.3 
867.8 

416.1 
438.5 
460.9 

445.8 
474.2 



507.4 

352.2 
359.1 
366.0 

444.4 
466.8 
489.2 
511.6 

473.9 
496.3 
518.7 
541.1 
563.5 

504.7 
527.1 
549.5 
571.9 
594.3 

559.1 
581.5 
603.9 
626.3 
648.7 

592.5 

474.1 
502.5 

503.6 
532.0 
560.3 

536.9 

•  •  •  •  • 

534.4 
562.8 
591.1 

567.7 
602.7 

452.1 
462.0 
471.9 
481.8 
491.7 

484.1 
494.0 
503.9 
513.8 
523.7 





594.8 
623.1 
651.5 

628.2 

634.7 

668.  1 

::::: 

546.3578.1 
558.9595.3 
571.5612.4 
584.1J629.6 
596.7i646.7 

568.2595.5 
580.8612.6 
593.4629.8 
606.0;646.9 
618.6664.1 
631.2  681.2 

604.0631.3 
616.6  648.4 

614.9 
637.3 
659.7 
682.1 
704.5 

627.0 
649.4 
671.8 
694.2 
716.6 
739.0 

662.8 
685.2 

656.5 
684.9 
713.2 

703.1 



527.4 
537.3 
547.2 
557.1 
567.0 

561  .9 
571.8 
581.7 
591.6 
601.5 

::::: 

662.7 
691.0 
719.4 

747.7 

698.5 
726.8 

702.6 
737.6 

738.4 
773.4 

!  '.'.'. 

:  :  :  :  : 

629.2 
641.8 
654.4 
667.0 

665.6 
682.7 
699.9 
717.0 

66S  4 

707.6 
730.0 
752.4 
774.8 

699.9 

755.2 
783.5 
811.9 

735.6 

808.4 

607.6 
617.5 
627.4 
637.3 

775.5 



g 

653.7685.5 
666.3702.7 
678.91719.8 
691.51  737.0 
704.1  754.1 
716.7771.3 

722.3 
744.7 
767.1 
789.5 
811.9 
834.3 

763.9 
792.3 
820.6 
849.0 
877.3 

810.5 
845.5 
880.5 

644.7 
654.6 
664.5 
674.4 
684.3 

173 


COLUMNS 


TABLE  43 


SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
LOS  ANGELES  AND  MILWAUKEE  BUILDING 
CODE  REQUIREMENTS 

fc=800 

jgaa* 

IP  I 

Size 
of 
column 
(inches) 

Diameter      Number 
of                    of 

(inches)            rod8 

! 

Square  rods 

Round  rods 

M 

H 

K 

1 

IK 

I* 

M 

K 

H 

1 

1M 

1M 

34 
35 
36 

37 
38 
3!) 
40 
41 

31                    14 
16 
18 
20 
22 
24 

32                    14 
16 
18 
20 
22 
24 

33                    14 
16 
18 
20 
22 
24 
26 

34                    14 
16 
18 
20 
22 
24 
26 

35                    14 
16 
18 
i          20 
22 
24 
26 

36                    16 
18 
20 

;       22 

24 

26 

28 

37                   16 
18 
20 
22 
24 
26 
28 

38                    16 
18 
!          20 
22 
24 
26 
28 
30 



::::: 

692.0 
704.6 
717.2 
729.8 
742.4 
755.0 

723.8 
741.0 
758.1 
775.3 
792.4 
809.6 

763.4 
780.6 
797.7 
814.9 
832.0 
849.2 

804.2 

760.6 
783.0 
805.4 
827.8 
850.2 
872.6 

800.2 
822.6 
845.0 
867.4 
889.8 
912.2 

841.0 

802.2 
830.6 
858.9 
887.3 
915.6 

848.8 
883.8 
918.8 



692!  9 
702.8 
712.7 
722.6 

698.1 
711.6 
725.0 
738.5 
752.0 
765.4 

737.7 
751.2 
764.6 
778.1 
791.6 
805.0 

727.0 
744.5 
762.1 
779.7 
797.3 
814.9 

766.6 
784.1 
801.7 
819.3 
836.9 
854.5 

807.4 
824.9 
842.5 
860.1 
877.7 
895.3 
912.9 

849.5 
867.0 
884.6 
902.2 
919.8 
937.4 
955.0 

892.9 
910.4 
928.0 
945.6 
963.2 
980.8 
998.4 

955.0 
972.6 
990.2 
1008 
1025 
1043 
1061 

1001 
1019 
1036 
1054 
1071 
1089 
1107 

1048 
1066 
1083 
1101 
1118 
1136 
1154 
1171 

759.7 
781.9 
804.2 
826.5 
848.7 
871.0 

799.3 
821.5 

843.8 
866.1 
888.3 
920.6 

840.1 
862.3 
884.6 
906.9 
929.1 
951.4 
973.7 

882.2 
904.4 
926.7 
949.0 
971.2 
993.5 
1016 

925.6 
947.8 
970.1 
992.4 
1015 
1037 
1059 

992.4 
1015 
1037 
1059 
1082 
1104 
1126 

1038 
1061 
1083 
1105 
1127 
1150 
1172 

1085 
1108 
1130 
1152 
1175 
1197 
1219 
1241 

796.2 
823.7 
851.2 
878.6 
906.1 
933.6 

835.8 
863.3 
890.8 
918.2 
945.7 
973.2 

876.6 
904.1 
931.6 
959.0 
986.5 
1014 
1041 

918.7 
946.2 
973.7 
1001 
1029 
1056 
1084 

962.1 
989.6 
1017 
1045 
1072 
1100 
1127 

1034 
1062 
1089 
1117 
1144 
1172 
1199 

1080 
1108 
1135 
1163 
1190 
1218 
1245 

1127 
1155 
1182 
1210 
1237 
1265 
1292 
1320 

841.8 
870.2 
898.5 
926.9 
955.2 
983.6 

882.6 

888.4 
923.4 
958  4 

993.4 



929.2 

821.4 
838.5 
855.7 
872.8 
890.0 
907.1 

846.3 
863.5 
880.6 
897.8 
914.9 
932.1 
949.2 

889.7 
906.9 
924.0 
941.2 
958.3 
975.5 
992.6 

951.5 
968.6 
985.8 
1003 
1020 
1037 
1054 

997.4 
1015 
1032 
1049 
1066 
1083 
1100 

1045 
1062 
1079 
1096 
1113 
1130 
1147 
1165 

863.4 
885.8 
908.2 
930.6 
953.0 
975.4 

883.1 
905.5 
927.9 
950.3 
972.7 
995.1 
1018 

926.5 
948.9 
971.3 
993.7 
1016 
1039 
1061 

993.5 
1016 
1038 
1061 
1083 
1106 
1128 

1039 
1062 
1084 
1107 
1129 
1151 
1174 

1087 
1109 
1131 
1154 
1176 
1199 
1221 
1243 

911.0 
939.3 
967.7 
996.0 
1024 
1053 

924.7 
953.1 
981.4 
1010 
1038 
1067 
1095 

968.1 
996.5 
1025 
1053 
1082 
1110 
1138 

1041 
1069 
1098 
1126 
1155 
1183 
1211 

1087 
1115 
1144 
1172 
1200 
1229 
1257 

1134 
1162 
1191 
1219 
1248 
1276 
1304 
1333 

964.2 
999.2 
1034 

971.3 
1006 
1041 
1076 
1111 

••••• 

792.0 
805.4 
818.9 
832.4 
845.8 
859.3 

834  !i 

847.5 
861.0 
874.5 
887.9 
901.4 

877  '.5 
890.9 
904.4 
917.9 
931.3 
944.8 

••••• 





1015 
1050 
1085 
1120 
1155 
1190 

1094 
1129 
1164 
1199 
1234 
1269 

1140 
1175 
1210 
1245 
1280 
1315 



935.5 
949.0 
962.5 
975.9 
989.4 
1003 

••••• 

••••• 

981.4 
994.9 
1008 
1022 
1035 
1049 

1187 
1222 
1257 
1292 
1327 
1362 
1397 





1042 
1056 
1069 
1082 
1096 
1109 

174 


TABLE  43 


COLUMNS 


ROUND  CORED  HOOPED  COLUMNS 


-srr^ 

SAFE  LOAD  IN  THOUSANDS  OF  POUNDS 
LOS  ANGELES  AND  MILWAUKEE  BUILDING 
CODE  REQUIREMENTS 

P  =  Afe[l  +  (n-l)p]                     ? 

fc 

=  15 

snn 

IP 

^^j&r 

—  ouv 

Size 
of 
column 
(inches) 

Diameter 
of 
core 
(inches) 

Number 
of 
rods 

Square  rods 

Round  rods 

H 

H 

H 

1 

IK 

IK 

H 

H 

H  '  i 

m 

lA 

42 
43 

44 
45 
46 
47 
48 
49 

39 
40 

41 
42 
43 
44 
45 
46 

16 
18 
20 
22 
24 
26 
28 
30 

16 
18 
20 
22 
24 
26 

1093 
1110 
1127 
1144 
1162 
1179 
1196 
1213 

1135 
1157 
1180 
1202 
1225 
1247 
1269 
1292 

1185 
1207 
1229 
1252 
1274 
1297 
1319 
1341 

1258 
1280 
1303 
1325 
1347 
1370 
1392 

1310 
1332 
1355 
1377 
1400 
1422 
1444 

1363 
1386 
1408 
1431 
1453 
1475 
1498 

1418 
1440 
1463 
1485 
1508 
1530 
1552 

1474 
1496 
1519 
1541 
1563 
1586 
1608 

1554 
1576 
1598 
1621 
1643 
1666 

1183 
1211 
1239 
1268 
1296 
1324 
1353 
1381 

1232 
1260 
1289 
1317 
1346 
1374 
1402 
1431 

1311 
1340 
1368 
1396 
1425 
1453 
1481 

1363 
1392 
1420 
1449 
1477 
1505 
1534 

1417 
1445 
1474 
1502 
1530 
1559 
1587 

1472 
1500 
1528 
1557 
1585 
1613 
1642 

1527 
1556 
1584 
1613 
1641 
1669 
1698 

1613 
1641 
1670 
1698 
1726 
1755 

1236 
1271 
1306 
1341 
1376 
1411 
1446 
1481 

1285 
1320 
1355 
1390 
1425 
1460 
1495 
1530 

1371 
1406 
1441 
1476 
1511 
1546 
1581 

1423 
1458 
1493 
1528 
1563 
1598 
1633 

1477 
1512 
1547 
1582 
1617 
1652 
1687 

1531 
1566 
1601 
1636 
1671 
1706 
1741 

1587 
1622 
1657 
1692 
1727 
1762 
1797 

1680 
1715 
1750 
1785 
1820 
1855 

I 

1096 
1114 
1132 
1149 
1167 
1184 
1202 
1220 

1146 
1164 
1181 
1199 
1216 
1234 
1252 
1269 

1215 
1232 
1250 
1267 
1285 
1303 
1320 

1267 
1284 
1302 
1319 
1337 
1355 
1372 

1134 
1156 
1178 
1201 
1223 
1245 
1267 
1290 

1183 
1206 
1228 
1250 
1273 
1295 
1317 
1339 

1257 
1279 
1301 
1323 
1346 
1368 
1390 

1309 
1331 
1353 
1376 
1398 
1420 
1442 

1362 
1385 
1407 
1429 
1451 
1474 
1496 

1417 
1439 
1461 
1484 
1506 
1528 
1550 

1473 
1495 
1517 
1540 
1562 
1584 
1606 

1552 
1574 
1597 
1619 
1641 
1664 

1176 
1203 
1231 
1258 
1286 
1313 
1341 
1368 

1225 
1253 
1280 
1308 
1335 
1363 
1390 
1418 

1304 
1331 
1359 
1386 
1414 
1441 
1469 

1356 
1383 
1411 
1438 
1466 
1493 
1521 

1409 
1437 
1464 
1492 
1519 
1547 
1574 

1464 
1491 
1519 
1546 
1574 
1601 
1629 

1520 
1547 
1575 
1602 
1630 
1657 
1685 

1604 
1632 
1659 
1687 
1714 
1742 



••'••• 

1104 
1117 
1131 
1144 
1158 

• 

• 

1160 
1177 
1194 
1211 
1228 
1245 
1262 

1211 
1228 
1245 
1262 
1279 
1296 
1313 

1154 
1167 
1180 
1194 
1207 



28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

18 
20 
22 
24 
26 
28 
30 

20 
22 
24 
26 
28 
30 



..... 



1204 
1218 
1231 
1245 
1258 





•-••• 

1280 
1297 
1314 
1331 
1348 
1366 



'i270 
1283 
1297 
1310 

|  

:::•! 

••:•:•:•. 

1333 
1350 
1368 
1385 
1402 
1419 

:::::;:::: 

'i337 
1351 
1364 

1338 
1355 
1373 
1391 
1408 
1426 





1388 
1405 
1422 
1439 
1457 
1474 

1392 
1410 
1428 
1445 
1463 
1480 

•  ••••••••• 

1392 
1405 
1418 

1461 
1478 
1495 
1512 
1530 



1466 
1483 
1501 
1519 
1536 

:::::  ::::: 

1461 
1474 



i 



1518 
1535 
1552 
1570 
1587 



1523 
1541 
1558 
1576 
1593 

1518 
1532 

175 


COLUMNS 


TABLE 


AREAS  AND  WEIGHTS  OF  COLUMN  RODS 


Number  of  rods 

Area  of  column  rods 

Number  of  rods 

Weight  of  column  rods  per  linear  foot 

Size  of  rods 

Size  of  rods 

H 

H 

M 

1 

IK 

IH 

H 

K 

H 

1 

IH 

i* 

4 

1.56 

2.25 

3.06 

4.00 

5.06 

6.25 

4 

5.313 

7.650 

10.41 

13.60 

17.21 

21.25 

6 

2.34 

3.38 

4.59 

6.00 

7.59 

9.38 

6 

7.969 

11.48 

15.62 

20.40 

25.82 

31.88 

8 

3.13 

4.50 

6.12 

8.00 

10.1 

12.5 

8 

10.63 

15.30 

20.82 

27.20 

34.42 

42.50 

10 

3.91 

5.63 

7.66 

10.0 

12.7 

15.6 

10 

13.28 

19.13 

26.03 

34.00 

43.03 

53.13 

1 

12 
14 

4.69 
5.47 

6.75 

7.88 

9.19 
10.7 

12.0 
14.0 

15.2 
17.7 

18.8 
21.9 

12 
14 

15.94 
18.59 

22.95 
26.78 

31.24 
36.44 

40.80 
47.60 

51.64 
60.24 

63.75 

74.28 

£ 

16 

6.25 

9.00 

12.2 

16.0 

20.2 

25.0 

16 

21.25 

30.60 

41.65 

54  .  40 

68.85 

85.00 

1 

18 
20 

7.03 

7.81 

10.1 
11.3 

13.8 
15.3 

18.0 
20.0 

22.8 
25.3 

28.1 
31.3 

18 
20 

23.91 
26.56 

34.43 
38.25 

46.85 
52.06 

61.20 
68.00 

77.45 
86.06 

95.63 
106.3 

22 

8.59 

12.4 

16.8 

22.0 

27.8 

34.4 

22 

29.22 

42.08 

57.27 

74.80 

94.67 

116.9 

24 

9.38 

13.5 

18.4 

24.0 

30.4 

37.5 

24 

31.88 

45.90 

62   47 

81.60 

103.3 

127.5 

26 

10.2 

14.6 

19.9 

26.0 

32.9 

40.6 

26 

34.53 

49.73 

67.68 

88.40 

111.9 

138.1 

28 

10.9 

15.8 

21  .4 

28.0 

35.4 

43.8 

28 

37.19 

53  .  55 

72.89 

95.20 

120.5 

148.8 

30 

11.7 

16.9 

23.0 

30.0 

38.0 

46.9 

30 

39.84 

57.38 

78.09 

102.0 

129.1 

159.4 

4 

1.23 

1.77 

2.41 

3.14 

3.98 

4.91 

4 

4.172 

6.008 

8.178 

10.68 

13.52 

16.09 

6 

1.84 

2.65 

3.61 

4.71 

5.96 

7.36 

6 

6.259 

9.013 

12.27 

16.02 

20.28 

25.03 

8 

2.45 

3.53 

4.81 

6.28 

7.95 

9.82 

8 

8.345 

12.02 

16.36 

21.36 

27.04 

33.37 

10 

3.07 

4.42 

6.01 

7.85 

9.94 

12.3 

10 

10.43 

15.02 

20.44 

26.70 

33.80 

41.72 

12 

3.68 

5.30 

7.22 

9.42 

11.9 

14.7 

12 

12.52 

18.03 

24.53 

32.04 

40.56 

50.06 

14 

4.30 

6.19 

8.42 

11.0 

13.9 

17.2 

14 

14.60 

21.03 

28.62 

37.39 

47.31 

58.41 

16 

4.91 

7.07 

9.62 

12.6 

15.9 

19.6 

16 

16.69 

24.03 

32.71 

42.73 

54.07 

66  .  75 

c 

18 

5.52 

7.95 

10.8 

14.1 

17.9 

22.1 

18 

18.78 

27.04 

36.80 

48.07 

60.83 

75  09 

o 

tf 

20 

6.14 

8.84 

12.0 

15.7 

19.9 

24.5 

20 

20.86 

30.04 

40.89 

53.41 

67.59 

83.44 

22 

6.75 

9.72 

13.2 

17.3 

21.9 

27.0 

22 

22.95 

33.05 

44.98 

58.75 

74.35 

91.78 

24 

7.36 

10.6 

14.4 

18.8 

23.9 

29.4 

24 

25.03 

36.05 

49  07 

64.09 

81.11 

100.1 

26 

7.98 

11.5 

15.6 

20.4 

25.8 

31.9 

26 

27.12 

39.06 

53.15 

69.43 

87.87 

108.5 

28 

8.59 

12.4 

16.8 

22.0 

27.8 

34.4 

28 

29.21 

42.06 

57.24 

74.77 

94.63 

116.8 

30 

9.20 

13.3 

18.0 

23.6 

29.8 

36.8 

30 

31.29 

45.06 

61.33 

80.11 

110.4 

125.2 

176 


TABLE  45 


COLUMNS 


AREA,  VOLUME,  WEIGHT  AND  PERIMETER 

OF 
SQUARE,  ROUND  AND  OCTAGONAL  COLUMNS 


Square  columns 

Round  columns 

Octagonal  columns 

Diam- 
eter of 

Area 

Volume 

Weight 

Perim- 

Area 

Volume 

Weight 

Perim- 

Volume 

Weight 

Perim- 

(sq. 

(c.  f. 

(Ib. 

eter 

(sq. 

(c.f. 

(Ib. 

eter 

(c.f. 

(Ib. 

eter 

in.) 

per  ft.) 

per  ft.) 

(ft.) 

in.) 

per  ft.) 

per  ft.) 

(ft.) 

per  ft.) 

per  ft.) 

(ft.) 

10 

100 

0.69 

104 

3.3 

78.54 

0.55 

82 

2.62 

0.58 

86 

2.76 

11 

121 

0.84 

126 

3.7 

95.03 

0.66 

99 

2.88 

0.70 

104 

3.14 

12 

144 

1.00 

150 

4.0 

113.1 

0.79 

118 

3.14 

0.83 

124 

3.31 

13 

169 

1.17 

175 

4.3 

132.7 

0.92 

138 

3.40 

0.97 

146 

3.57 

14 

196 

1.36 

204 

4.7 

153.9 

1.07 

160 

3.66 

1.13 

169 

3.87 

15 

225 

1.56 

234 

5.0 

176.7 

1.23 

184 

3.93 

1.29 

194 

4.14 

16 

256 

1.78 

267 

5.3 

201.1 

1.40 

209 

4.18 

1.47 

221 

4.42 

17 

289 

2.01 

302 

5.7 

227.0 

1.58 

236 

4.45 

1.66 

249 

4.70 

18            324 

2.25 

338 

6.0 

254.5 

1.77 

265 

4.71 

1.86 

280 

4.97 

19            361 

2.51 

377 

6.3 

283.5 

1.97 

295 

4.97 

2.08 

312 

5.25 

20 

400 

2.78 

417 

6.7 

314.2 

2.18 

327 

5.23 

2.30 

345 

5.52 

21 

441 

3.06 

459 

7.0 

346.4 

2.41 

361 

5.50 

2.54 

381 

5.80 

22 

484 

3.36 

504 

7.3 

380.1 

2.64 

396 

5.76 

2.78 

418 

6.08 

2.3            529 

3.68 

552 

7.7 

415.5 

2.89 

433 

6.02 

3.04 

457 

6.35 

24       !      576 

4.00 

600 

8.0 

452.4 

3.14 

471 

6.28 

3.31 

497 

6.63 

2.~>            025 

4.34 

651. 

8.3 

490.9 

3.41 

511 

6.55 

3.60 

539 

6.90 

2(i            676 

4.69 

704_ 

8.7 

530.9 

3.69 

553 

6.81 

3.89 

583 

7.18 

27 

729 

5.06 

758 

9.0 

572.6 

3.98 

596 

7.07 

4.19 

629 

7.45 

28 

784 

5.44 

816 

9.3 

615.8 

4.28 

641 

7.33 

4.51 

677 

7.73 

29 

841 

5.84 

877 

9.7 

660.5 

4.59 

688 

7.58 

4.84 

726 

8.01 

30 

900 

6.25 

938 

10.0 

706.9 

4.91 

736 

7.86 

5.18 

777 

8.29 

31 

961 

6.67 

1000 

10.3      !   754.8 

5.24 

786 

8.12 

5.53 

829 

6.56 

32 

1024 

7.12 

1067 

10.7        804.2 

5.58 

838 

.8.38 

5.89 

884 

8.84 

33 

1089 

7.56 

1134 

11.0        855.3 

5.94 

891 

8.64 

6.27 

940 

9.11 

34 

1156 

8.02 

1203 

11.3      1  907.9 

6.30 

946 

8.89 

6.55 

983 

9.39 

35 

1225 

8.50 

1275 

11.7     I  962.1 

6.68 

1002 

9.16 

7.05 

1057 

9.67 

36 

1296 

9.00 

1350 

12.0 

1018 

7.07 

1060 

9.42 

7.46 

1118 

9.94 

37 

1369 

9.50 

1425 

12.3 

1075 

7.47 

1120 

9.68 

7.88 

1181    • 

10.22 

38 

1444 

10.03 

1505 

12.7 

1134 

7.88 

1181 

9.95 

8.31 

1246 

10.50 

39          1521 

10.57 

1586 

13.0 

1195 

8.30 

1244 

10.21 

8.75 

1313 

10.78 

40          1600 

11*11 

1666 

13.3 

1257 

8.73 

1309 

10.47 

9.21 

1381 

11.05 

41           1681 

11.68 

1753 

13.7 

1320 

9.17 

1375 

10.72 

9.67 

1451 

11.33 

42          1764 

12.25 

1839 

14.0 

1385 

9.62 

1443 

10.99 

10.15 

1522 

11.60 

43          1849 

12.84 

1926 

14.3 

1452 

10.08 

1513 

11.26 

10.64 

1596 

11   88 

44           1936 

13.45 

2020 

14.7 

1520 

10.56 

1584 

11.52 

11.14 

1671      j      12.17 

45          2025 

14.06 

2110 

15.0 

1590 

11.04 

1657 

11.79         11.65 

1748           12.43 

46          2116 

14.69 

2202 

15.3 

1662 

11.54 

1731 

12.04   !      12.17   :      1826 

12.70 

47       ;  2209 

15.34 

2300 

15.7 

1735 

12.05 

1807 

12.31   I      12.71 

1906 

12.98 

48 

2304 

16.01 

2400 

16.0 

1810 

12.57 

1885 

12.57   j      13.26 

1988 

13.26 

49 

2401 

16.68 

2502 

16.3 

1886 

13.10 

1964 

12.83   j      13.81 

2072 

13.53 

50 

2500 

17.36 

2604 

16.7 

1964 

13.64 

2045 

13.10  1      14.38 

2158 

13.81 

j 

177 


COLUMNS 

TABLE  46 

COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 
AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 

HEAVY  TYPE  GIVES  PERCENTAGES                                               WEIGHTS  DO  NOT  INCLUDE  SPACERS 
LIGHT  TYPE  GIVES  WEIGHTS                                                          WIRE  SIZES  ARE  A.  S.  &  W.  CO.  GAGE 

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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
LIGHT  TYPE  GIVES  WEIGHTS 


WEIGHTS  DO  NOT  INCLUDE  SPACERS 
WIRE  SIZES  ARE  A.  S.  &  W.  CO.  GAGE 


179 


COLUMNS 


TABLE  46 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY 
LIGHT 


TYPE 
TYPE 


GIVES  PERCENTAGES 
GIVES  WEIGHTS 


WEIGHTS  DO  NOT  INCLUDE  SPACERS 
WIRE  SIZES  ARE  A.  S.  &  W.  CO.  GAGE 


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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
LIGHT  TYPE  GIVES  WEIGHTS 


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WIRE  SIZES  ARE  A.  S.  &  W.  CO.  GAGE 


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COLUMNS 


TABLE  46 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
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COLUMNS 


TABLE  46 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE 
LIGHT  TYPE 


GIVES  PERCENTAGES 
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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
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TABLE  46 


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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
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TABLE  46 


COLUMN  SPIRALS 
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AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE 
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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
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COLUMNS 


TABLE  46 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
LIGHT  TYPE  GIVES  WEIGHTS 


WEIGHTS  DO  NOT  INCLUDE  SPACERS 
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TABLE  46 


COLUMNS 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
LIGHT  TYPE  GIVES  WEIGHTS 


WEIGHTS  DO  NOT  INCLUDE  SPACERS 
WIRE  SIZES  ARE  A.  S.  &  W.  CO.  GAGE 


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COLUMNS 


TABLE  46 


COLUMN  SPIRALS 
PERCENTAGE  OF  VOLUME  OF  CORE 

AND 
WEIGHT  IN  POUNDS  PER  FOOT  OF  COLUMN 


HEAVY  TYPE  GIVES  PERCENTAGES 
LIGHT  TYPE  GIVES  WEIGHTS 


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TABLE  47 


COLUMNS 


COLUMN  SPIRALS 
JOINT  COMMITTEE  RECOMMENDATIONS 


Volume  of  spiral  equal  to  1%  of  volume  of  core 


Maximum  pitch  =  -  or 

6 


m, 


Diam.  of  core 
(inches) 

Am.  S.  &  W.  Co.'s  gage                                                    Rod  sizes 

Size  (No.) 

Pitch  (inches)                  Size  (inches) 

Pitch  (inches) 

8 

6 

IK 

• 

9 

5 

IK 

10 

4 

IK 

11 

3 

IN 

X 

m 

12 

2 

i« 

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IH 

13 

1 

i« 

y* 

IX 

14 

1 

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2K 

15 

0 

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Xs 

2 

16 

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2K 

x* 

IK 

17 

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2 

H 

2K 

18 

3/0 

2X 

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2H 

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2K 

20 

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2K 

21 

4/0 

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2 

22 

4/0 

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7A* 

2H 

23 

4/0 

2H 

K* 

2% 

24 

4/0 

2 

7A6 

2H 

25 

5/0 

2K 

14s 

2K 

26 

5/0 

2K 

^6 

2y* 

27 

5/0 

2K 

H6 

2K 

28 

5/0 

2 

He 

2K 

29 

6/0 

2K 

Ke 

2 

30 

6/0 

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2 

31 

6/0 

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H 

2M 

32 

6/0 

2 

X 

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33 

7/0 

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H 

2H 

34 

7/0 

2K 

H 

2K 

35 

7/0 

2K 

y* 

2M 

36     . 

7/0 

2 

M 

2H 

37 

7/0 

2 

x 

2K 

38 

7/0 

2 

H 

2 

39 

7/0 

IK 

y* 

2 

40 

7/0 

IK 

y* 

IK 

41 

7/0 

IK 

y* 

IK 

42 

7/0 

i« 

y* 

IK 

43 

7/0 

IX 

H 

iH 

44 

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i% 

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m 

45 

7/0 

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H 

IK 

46 

7/0 

i% 

H 

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47 

7/0 

IK 

H 

i^ 

48 

7/0 

IK 

H 

i^ 

49 

7/0 

IK 

H 

IK 

50 

7/0 

IH 

X 

IK 

195 


COLUMNS 


TABLE  48 


AMERICAN  STEEL  &  WIRE  CO.'S  STEEL  WIRE  GAGE 


Diameter 
(inches) 

Steel  wire 
gage 

Diameter 

(inches) 

Area,  square 
inches 

Pounds  per 
foot 

Pounds  per 
mile 

Feet  per 
pound 

y> 

0  .  5000 

! 

0.19635                  0.6668 

3,521.0 

1.500 

7/0 

0.4900 

0.18857                  0.6404 

3,381.0 

1.562 

% 

0.46875 

0.17257                  0.5861 

3,094.0 

1.706 

6/0 

0.4615 

0.16728                  0.5681 

2,999.0 

1.760 

He 

0.4375 

0.15033                  0.5105 

2,696.0 

1.959 

5/0 

0.4305 

0.14556 

0.4943 

2,610.0 

2.023 

13|2 

0.40625 

0.12962 

0.4402 

2,324.0 

2.272 

4/0 

0.3938 

0.12180 

0.4136 

2,184.0 

2.418 

H 

0  .  3750 

0.11045 

0.3751 

1,980.0 

2.666 

3/0 

0.3625 

0.10321 

0.3505 

1,851.0 

2.853 

11,^2 

0.34375 

0.092806 

0.3152 

1,664.0 

3.173 

2/0 

0.3310 

0.086049                0.2922 

1,543.0 

3.422 

Me 

0.3125 

0.076699 

0.2605 

1,375.0 

3.839 

0 

0  .  3065 

0.073782 

0.2506 

1,323.0 

3.991 

1 

0.2830 

0.062902 

0.2136 

1,128.0 

4.681 

%a 

0.28125 

0.062126 

0.2110 

1,114.0 

4.74 

2 

0.2625 

0.054119 

0.1838 

970.4 

5.441 

^ 

0  .  2500 

0.049087 

0.1667 

880.2 

5.999 

3 

0.2437 

0.046645 

0  .  1584 

836.4 

6.313 

4 

0.2253 

0.039867 

0.1354 

714.8 

7.386 

3-32 

0.21875 

0.037583 

0.1276 

673.9 

7.835 

] 

5 

0.2070                 0.033654 

0.1143 

603.4 

8.750 

6 

0.1920                 0.028953 

0.09832 

519.2' 

10.17 

He 

0.1875                 0.027612 

0.09377 

495.1 

10.66 

7 

0.177(»                 0.024606 

0.08356 

441.2 

11.97 

8 

0.162C 

0.020612 

0.07000 

369.6 

14.29 

%2 

0.15625 

0.019175 

0.06512 

343.8 

15.36 

9 

G.1483 

0.017273 

0.05866 

309.7 

17.05 

10 

0.1350 

0.014314 

0.04861 

356.7 

20.57 

« 

0.125 

0.012272 

0.04168 

220.0 

24.00 

If 

0.1205 

0.011404 

0.03873 

204.5 

25.82 

12 

0.1055 

0.0087417 

0.02969 

156.7 

33.69 

Ma 

0.09375 

0  .  0069029 

0.02344 

123.8 

42.66 

13 

0.0915 

0.0065755 

0.02233 

117.9 

44.78 

14 

0.0800 

0  .  0050266 

0.01707 

90.13 

58.58 

15 

0.0720 

0.0040715 

0.01383 

73.01 

72.32 

16 

0.0625 

0.0030680 

0.01042 

55.01 

95.98 

17 

0.0540 

0  .  0022902 

0.007778 

41.07 

128.60 

196 


JJ1AUKAM   42 

WEIGHT  OF  TYPICAL  SQUARE  PANEL  OF  THREE-BE 
FLOOR  SYSTEM  DESIGNED  IN  ACCORDANCE  WITH  J 
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COLUMNS 


DIAGRAM  43 


WEIGHT  OF  TYPICAL  FLOOR  PANEL  OF  FLAT  SLAB  CONSTRUCTION 

DESIGNED  IN  ACCORDANCE  WITH  CHICAGO  BUILDING  CODE 

(FOR  ESTIMATING  COLUMN  LOADS) 


Column  spacing  in  feet 


SECTION  8 
BENDING  AND  DIRECT  STRESS 


Rectangular  Sections 

The  following  notation  is  used  : 

R  =  resultant  thrust. 

N  =  vertical  component  of  R. 

x0  =  eccentricity  of  thrust. 
t  =  thickness  or  depth  of  section. 

6  =  breadth  of  section. 

d'  =  embedment  of  steel  —  top  and  bottom. 
As  =  area  of  steel  on  tension  side. 
A'  =  area  of  steel  on  compression  side. 
Ao  =  total  area  of  steel  =  Aa  +  A'. 

p0  =  total  percentage  of  steel  =  r-r- 

fc  =  maximum  unit  compression  in  concrete. 
fa  =  maximum  unit  tension  in  steel. 
//  =  maximum  unit  compression  in  steel. 

Case  I.  —  Compression  Over  Whole  Section  (A'  =  As}. 

ir$ 

Diagrams  44  to  49  inclusive  give  values  of  K  for  various  values  of  p0,  -~i  and-—, 

and  for  both  n  =  12  and  n  =  15.     For  values  of  ~  beyond  the  termination  of  the 

curves,  tension  occurs  over  part  of  the  section  and  the  diagrams  for  Case  II  should 
be  used. 

Case  n.  —  Tension  Over  Part  of  Section  (A'  =  As). 


Diagrams  50,  51,  52,  54,  55  and  56  give  values  of  k  for  various  values  of  p0,  —  ,  and 

y>  and  for  both  n  =  12  and  n  =  15.     Diagrams  53  and  57  give  values  of  L. 

The  method  of  procedure  in  solving  problems  is  as  follows:  (1)  Determine  k  from 
the  proper  diagram;  (2)  find  L  from  Diagram  53  or  57;  (3)  solve  equation  (2)  for/c; 
(4)  find  unit  stresses  in  the  steel  from  the  formulas 

(3) 

(4) 
199 


-  BENDING  AND  DIRECT  STRESS 

Case  III.  —  Tension  Over  Part  of  Section  (A'  =  0).     Notation  is  given  on  Dia- 
grams 58  and  59. 

k*  -2pn(l  -  A;)  =  k*jde,  (5) 

3  =  1-  lAk  (6) 


(8) 


/•     -    ™/c  (10) 

Diagrams  58  and  59  may  be  used  as  shown  in  two  of  the  examples  which  follow. 

Examples  for  Rectangular  Sections 

A  beam  is  9  in.  wide  and  20  in.  deep.  The  reinforcement  both  above  and  below 
consists  of  one  steel  rod  1  in.  in  diameter  embedded  at  a  depth  of  2  in.  At  a  certain 
section,  the  normal  component  of  the  resultant  force  is  60,000  lb.,  acting  at  a  distance  of  3  A 
in.  from  the  gravity  axis.  Assume  n  —  15.  Compute  the  maximum  unit  compressive 
stress  in  the  concrete. 

A0_  (2)  (0.7854)  _ 


__ 

Po  ~         ~ 


bt  ~       (9)(20 


dr  =  O.lOi 

For  these  values  of  p0  and  —  ,  Diagram  48  gives  K  =  1.70  and  shows  that  the 

problem  falls  under  Case  I.     Then  by  formula  (1) 
NK      (60,  000)  (1.70) 


(9)  (20)          =  567  Ib.  per  sq.  in. 
Change  the  eccentricity  of  the  preceding  problem  to  6  in.  and  solve. 


/£    ,  /v» 

For  p,  =  0.0087  and  -r  =  0.30,  Diagram  48  shows  that  y  is  too  great  for  the 

problem  to  come  under  Case  I.     The  method  of  procedure  for  Case  II  must  then  be 
followed. 

Diagram  55  gives  k  =  0.73  for  the  values  of  p0  and  -y  given  above.     With  k  = 
0.73  and  p0  =  0.0087,  Diagram  57  shows  L  to  be  0.123.     Solving  equation  (2) 

M  (60,000;(6) 

fc  =  LbT*  =  (0.123)(9)(20)«  =  815  lb'  Per  Sq'  in' 
Using  formula  (3) 


/.  -  nfc  (~-t  -  l)  =  (15)  (815)  (0-73—20  -  l)  =  283°  lb-  Per  sq-  in. 

The  stress  /,'  may  be  found  by  formula  (4)  but  is  always  less  than  n  X  fc- 

An  arch  is  20  in.  deep  and  is  reinforced  with  three  rods  %  in.  in  diameter  to  each 
foot  of  width,  both  above  and  below.  If  the  rods  are  embedded  to  a  depth  of  2  in.  and  the 
normal  component  of  the  resultant  thrust  on  a  section  is  100,000  lb.  for  1-ft.  width  of  arch. 

200 


BENDING  AND  DIRECT  STRESS 

ivith  an  eccentricity  of  3.4  in.,  determine  the  maximum  intensity  of  compressive  stress  on 
the  concrete.     Assume  n  —  15. 

(6)  (0.4418) 
Po=  - 


Diagram  48  gives  K  =  1.63  and  the  problem  comes  under"  Case  I.     Then  by 
formula  (1) 

NK      (100,000)(1.63)       a_nlu 

'-! 


The  vertical  wall  of  a  cantilever  retaining  wall  is  subjected  to  an  earth  pressure  of 
2400  Ib.  applied  at  a  distance  of  4.54  ft.  above  the  top  of  footing.     The  weight  of  vertical 
wall  is  2200  Ib.  which  can  be  considered  as  applied  5  in.  in  front  of  the  steel.     Determine 
the  unit  stresses  fc  andfs,  assuming  n  =  15,  p  =  0.0077  and  d  =  10.5  in. 
The  moment  at  the  top  of  footing 

M  =  (2400)  (4.54)  (12)  +  (2200)  (5)  =  141,700  in.  -  Ib. 
=  _141,700_ 
(12)(10.5)2 
e^  141,700 

d        (2200)  (10.5) 

Entering  Diagram  59  with  a  value  of  p  =  0.0077  on  the  lower  right-hand  margin 

pt 

and  tracing  vertically  to  a  value  of  -r  =  6.1,  then  horizontally  to  the  left  to  a  point 

vertically  above  K  =  107,  we  find  /.  =  14,000  and  fc  =  610. 

Design  the  vertical  watt  of  the  retaining  wall  described  in  the  preceding  problem 
so  thatff  =  750  and  /,  =  16,000.     Assume  the  weight.  of  wall  to  be  2000  Ib. 

For  these  unit  stresses  the  left-hand  part  of  Diagram  59  shows  K  =  133.8.     Then 


d  =  V(133!s)(12)  =  9'4  ^  Say  9^  in' 

«:  =  _Hi,70o_ 

d       (2000)  (9.5) 

Following  across  the  diagram  horizontally  to  the  right  to  a  value  of  -r  =  7.45  and  then 
vertically  downward  to  the  lower  right-hand  margin,  we  find  p  =  0.0085. 

Round  Columns 
Concrete  outside  of  the  hooping  is  neglected.     The  following  notation  is  used: 

P  =  direct  load  (compression). 

e  =  eccentricity  of  load. 

r  =  radius  of  column  core. 

p  =  total  percentage  of  steel. 
fe  =  maximum  unit  compression  in  concrete. 
fc    =  minimum  unit  compression  in  concrete. 
fs  =  maximum  unit  tension  in  steel. 
/.'  =  maximum  unit  compression  in  steel. 


Case  I. — Compression  Over  Whole  Section. — Diagram  60  gives  values  of 

for  various  values  of  p  and  — ,  and  for  both  n  =  12  and  n  =  15. 

201 


BENDING  AND  DIRECT  STRESS 
Case  II.  —  Tension  Over  Part  of  Section. 

*- 


r> 

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Jc 

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R 

formula  (12). 

Case  III.  —  Bending  Only. 

*- 


ff  f? 

Values  of  j  and  -7-  in  the  preceding  equations  are  given  in  Diagram  63.     Diagram 

J  c  J  s 

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the  familiar  diagrams  for  rectangular  sections  with  steel  in  tension  side  only.     In  the 

present  case  the  value  of  —  ;  is  used  instead  of  T-TO' 
irr3  bd2 

Examples  for  Round  Columns 

Assuming  a  column  with  2Q-in.  core  reinforced  with  ten  l-in.  square  rods  and  sus- 
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in  the  concrete,  n  =  15. 

10  e         2 

r  =  10  in.          „  -  (angexioy  =  0.0318  r  =  Fd  -  °-2° 

From  Diagram  60 


or 

1.12P        224,000 

~i^~     "  "31TT6    =  712  lb'  PW*  Sq"  m- 

Find  the  maximum  unit  stresses  in  the  concrete  and  steel  of  the  column  in  the  preceding 
problem  if  the  eccentricity  of  the  load  is  8  in. 


r  =  10  in.          p  =  0.0318         -   =         =  1.25 

8 


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?  =  0.325 


R  -  ^  -  1>600>000  -  r) 
"  irr*  ~      3141.6 

fc  =        ~    =  0^25  =  1)56 


/,  =  25R  =  (25)  (509)  =  12,720  lb.  per  sq.  in. 
f/  =  nfc  =  23,500  lb.  per  sq.  in. 


202 


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212 


DIAGRAM  54 


BENDING 

AND 
DIRECT  STRESS 


RECTANGULAR  SECTIONS—  TENSION  OVER  PART  OF  SECTION 

VALUES  OF  k  dn=°155t 

A'=A, 


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213 


BENDING 

AND 
DIRECT  STRESS 


DIAGRAM  55 


d'=0.10t 
n  =  15 

A'=A3 


RECTANGULAR  SECTIONS— TENSION  OVER  PART  OF  SECTION 

VALUES  OF  k 


$ 

"6 

& 

fe 


IMilUSl 


m\ 


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a  j.o 


214 


DIAGRAM  56 


BENDING 

AND 
DIRECT  STRESS 


RECTANGULAR  SECTIONS—  TENSION  OVER  PART  OF  SECTION 

d 
VALUES  OF  k 


'  =  0.15t 
n=15 


BENDING 

AND 
DIRECT  STRESS 


DIAGRAM  57 


RECTANGULAR  SECTIONS— TENSION  OVER  PART  OF  SECTION 

M 


DIAGRAM  58 


BENDING 

AND 
DIRECT  STRESS 


RECTANGULAR  SECTIONS— TENSION  OVER  PART  OF  SECTION 

STEEL  IN  TENSION  FACE  ONLY 

VALUES  OF  fc,  f,  AND  p 


n  =  12 
A'=0 


217 


BENDING 

AND 
DIRECT  STRESS 


DIAGRAM  5! 


RECTANGULAR  SECTIONS— TENSION  OVER  PART  OF  SECTION 

STEEL  IN  TENSION  FACE  ONLY 

VALUES  OF  fc,  fs  AND  p 


DIAGRAM  60 


BENDING 

AND 
DIRECT  STRESS 


ROUND  COLUMNS— COMPRESSION  OVER  WHOLE  SECTION 
VALUES  OF 


n=12 
n=15 


219 


BENDING 

AND 
DIRECT  STRESS 


DIAGRAM  61 


ROUND  COLUMNS—  TENSION  OVER  PART  OF  SECTION 


n=12 


VALUES  OF      AND- 
ic  K 


DIAGRAM  62 


BENDING 

AND 
DIRECT  STRESS 


ROUND  COLUMNS— TENSION  OVER  PART  OF  SECTION 

VALUES  OF  ^  AND  4 
tc  K 


n=15 


BENDING 
AND 
DIRECT  STRESS 

DIAGRAM  63 

ROUND  COLUMNS—  BENDING  ONLY 

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222 


DIAGRAM  64 


BENDING 

AND 
DIRECT  STRESS 


ROUND  COLUMNS— BENDING  ONLY 
VALUES  OF  R,  fs,  fe  AND  p 


=  12 
=  15 


223 


SECTION  9 
FOOTINGS 

Diagram  65  makes  it  possible  to  find  readily  the  bending  moments  which  occur  at 
each  face  of  column  for  both  square  and  rectangular  footings.  The  illustrations 
above  this  diagram  show  how  the  diagram  is  used.  For  example,  suppose  the  bending 
moment  is  required  at  the  face  of  a  24-in.  column  supporting  a  load  of  300,000  Ib. 
and  resting  on  a  footing  9  ft.  2  in.  square.  From  the  upper  part  of  Diagram  65,  C\  = 
6.2  and 

M  =  (6.2)  (300,000)  =  1,860,000  in.-lb. 

Tables  49,  50  and  51,  based  on  the  recommendations  contained  in  Bulletin  67  of 
the  University  of  Illinois  Engineering  Experiment  Station,  give  the  design  of  square 
reinforced  footings  for  different  loads,  column  sizes  and  soil  pressure.  These  footings 
are  without  offsets  and  for  large  footings  it  will  usually  be  found  more  economical  to 
use  one  or  two  offsets. 

These  tables  are  computed  for  square  columns.  If  round  columns  are  used, 
multiply  the  diameter  by  0.7854  to  get  the  size  of  square  columns  of  equivalent 
perimeter  and  enter  the  table  with  that  size. 

The  recommendations  in  the  bulletin  mentioned  above  are  as  follows: 

Width  of  Footing  to  Use  in  Flexure  Computations  for  Two-way  Reinforcement. — 
With  two-way  reinforcement  evenly  spaced  over  the  footing,  it  seems  that  the  tensile 
stress  is  approximately  the  same  in  bars  lying  within  a  space  somewhat  greater  than 
the  width  of  the  pier  and  that  there  is  also  considerable  stress  in  the  bars  which  lie 
near  the  edges  of  the  footing.  For  intermediate  bars  stresses  intermediate  in  amount 
will  be  developed.  For  footings  having  two-way  reinforcement  spaced  uniformly 
over  the  footing,  the  method  proposed  for  determining  the  maximum  tensile  stress  in 
the  reinforcing  bars,  is  to  use  in  the  calculation  of  resisting  moment  at  a  section  at  the 
face  of  the  pier  the  area  of  all  the  bars  which  lie  within  a  width  of  footing  equal  to  the 
width  of  pier  plus  twice  the  thickness  of  footing,  plus  half  the  remaining  distance  on 
each  side  to  the  edge  of  the  footing.  This  method  gives  results  in  keeping  with  the 
results  of  tests.  When  the  spacing  through  the  middle  of  the  width  of  the  footing  is 
closer,  or  even  when  the  bars  are  concentrated  in  the  middle  portion,  the  same  method 
may  be  applied  without  serious  error.  Enough  reinforcement  should  be  placed  in  the 
outer  portion  to  prevent  the  concentration  of  tension  cracks  in  the  concrete  and  to 
provide  for  other  distribution  of  stress. 

No  failures  of  concrete  have  been  observed  in  tests  and  none  would  be  expected 
with  the  low  percentages  of  reinforcement  used. 

Bond  Stresses. — The  method  proposed  for  calculating  maximum  bond  stress  in 
column  footings  having  two-way  reinforcement  evenly  spaced,  or  spaced  as  npted  in  the 
preceding  paragraph,  is  to  use  the  ordinary  bond  stress  formula,  and  to  consider  the 
circumference  of  all  the  bars  which  were  used  in  the  calculation  of  tensile  stress,  and 
to  take  for  the  external  shear  that  amount  of  upward  pressure  or  load  which  was  used 
hi  the  calculation  of  the  bending  moment  at  the  given  section. 

Bond  resistance  is  one  of  the  most  important  features  of  strength  of  column 
footings,  and  probably  much  more  important  than  is  appreciated  by  the  average 

225 


FOOTINGS 

designer.  The  calculations  of  bond  stress  in  footings  of  ordinary  dimensions-  where 
large  reinforcing  bars  are  used  show  that  the  bond  stress  may  be  the  governing  element 
of  strength.  Tests  show  that  in  multiple-way  reinforcement  a  special  phenomenon 
affects  the  problem  and  that  lower  bond  resistance  may  be  found  in  footings  than  in 
beams.  Longitudinal  cracks  form  under  and  along  the  reinforcing  bar  due  to  the 
stretch  in  the  reinforcing  bars  which  extend  in  another  direction,  and  these  cracks  act 
to  reduce  the  bond  resistance.  The  development  of  these  cracks  along  the  reinforcing 
bars  must  be  expected  in  service  under  high  tensile  stresses,  and  low  working  bond 
stresses  should  be  selected.  An  advantage  will  be  found  in  placing  under  the  bars  a 
thickness  of  concrete  of  2  in.,  or  better  3  in.,  for  footings  of  the  size  ordinarily  used  in 
buildings. 

Difficulty  may  be  found  in  providing  the  necessary  bond  resistance,  and  this  points 
to  an  advantage  in  the  use  of  bars  of  small  size,  even  if  they  must  be  closely  spaced. 
Generally  speaking,  bars  of  %-in.  size  or  smaller  will  be  found  to  serve  the  purpose  of 
footings  of  usual  dimensions.  The  use  of  large  bars,  because  of  ease  in  placing,  leads 
to  the  construction  of  footings  which  are  insecure  in  bond  resistance.  Column  footings 
reinforced  with  deformed  bars  develop  high  bond  resistance.  Curving  the  bar  upward 
and  backward  at  the  end  increases  the  bond  resistance,  but  this  form  is  awkward  in 
construction.  Reinforcement  formed  by  bending  long  bars  in  a  series  of  horizontal 
loops  covering  the  whole  footing  gives  a  footing  with  high  bond  resistance. 

The  use  of  short  bars  placed  with  their  ends  staggered  increases  the  tendency  to  fail 
by  bond  and  cannot  be  considered  as  acceptable  practice  in  footings  of  ordinary  pro- 
portions. In  footings  in  which  the  projection  is  short  in  comparison  with  the  depth, 
the  objection  is  very  great. 

Diagonal  Tension. — As  a  means  of  measuring  resistance  to  diagonal  tension  failure, 
the  vertical  shearing  stress  should  be  calculated  by  using  the  vertical  sections  formed 
upon  the  square  (assuming  square  column)  which  lies  at  a  distance  from  the  face  of  the 
pier  equal  to  the  depth  of  the  footing.  This  calculation  gives  values  of  the  shearing 
stress,  for  footings  which  failed  by  diagonal  tension,  which  agree  fairly  closely  with 
the  values  which  have  been  obtained  in  tests  of  simple  beams.  The  formula  used  in 

V 

this  calculation  is  v  =  rrj?  where  V  is  the  total  vertical  shear  at  this  section  taken  to 
ojd' 

be  equal  to  the  upward  pressure  on  the  area  of  the  footing  outside  of  the  section  con- 
sidered, b  is  the  total  distance  around  the  four  sides  of  the  section,  and  jd  is  the  dis- 
tance from  the  center  of  reinforcing  bars  to  the  center  of  the  compressive  stresses. 
The  working  stress  now  frequently  specified  for  this  purpose  in  the  design  of  beams, 
40  Ib.  per  sq.  in.,  for  1:2:4  concrete,  may  be  applied  to  the  design  of  footings. 


226 


DIAGRAM  65 


BENDING  MOMENTS  FOR  SINGLE  COLUMN  FOOTINGS 

.- d  


M=C,P 


•*«»•. 

EH 


LJi 


M-QdP 


M=CjdP 


Square  footings  with 

square  or  round  columns 

M  =  C,P   (in.-lh) 


Length  of  footing,  side    (b)  in  feet 


Rfictungjlar  fbalrnqs-for 
squan-  or  round  cofumns 

M-CjdP 
far  rectanular  columns 


Values  of    a/d    (or 


227 


FOOTINGS 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16, 000 


2  TONS  ON  SOIL 


TABLE  49 


Squart  column 


Footing 

size 
b 

Column 
size 
a 
(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 

(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
Ub.) 

(ft.) 

(in.) 

Square 

Round 

3 

0 

10 

34.8 

11 

H 

8 

10 

37.4 

8.3 

12 

"     34.9 

10 

9 

12 

42.0 

7.5 

14 

35.0 

9 

10 

13 

46.7 

6.8 

3 

6 

10 

46.9 

14 

M 

8 

10 

44.2 

14.3 

12 

47.2 

12 

10 

12 

55.2 

12.3 

14 

47.3 

11 

11 

13 

60.7 

,11.3 

4 

0 

10 

60.6 

17 

H 

8 

10 

51.0 

22.7 

12 

61.2 

14 

10 

13 

63.7 

18.7 

14 

61.4 

13 

11 

14 

70.1 

17.3 

16 

61.6 

12 

12 

15 

76.5 

16.0 

4 

6 

10 

75.9 

20 

H 

8 

10 

57.7 

33.8 

12 

76.7 

17 

10 

12 

72.2 

28.7 

14 

77.2 

15 

12 

15 

86.6 

25.3 

16 

77.7 

13 

14 

18 

101.0 

22.0 

5 

0 

10 

92.7 

23 

H 

8 

10 

64.6 

47.9 

12 

93.7 

20 

10 

12 

80.7 

41.7 

14 

94.4 

18 

11 

14 

88.8 

37.5 

16 

95.0 

16 

13 

16 

105 

33.4 

18 

95.6 

14 

16 

20 

129 

29.2 

5 

6 

10 

110.8 

27 

±2 

8 

10 

71.4 

68.0 

12 

112.8 

23 

10 

12 

89.2 

58.0 

14 

113.4 

20 

12 

15 

107 

50.4 

16 

114.2 

18 

13 

17 

116 

45.4 

18 

114.6 

17 

14 

18 

125 

42.8 

6 

0 

10 

130.1 

31 

H 

7 

9 

68.4 

93.0 

12 

131.8 

27 

9 

11 

88.0 

81.0 

14 

133.2 

24 

11 

14 

108 

72.0 

16 

134.5 

21 

13 

16 

127 

63.0 

18 

135.4 

19 

15 

19 

147 

57.0 

20 
22 

136.3 
136.8 

17 
16 

& 

17 
18 

22 
23 

166 
176 

51.0 
48.0 

6 

6 

10 

150.5 

35 

M 

8 

10 

85 

123.0 

12 

153.1 

30  • 

10 

12 

106 

106.0 

14 

154.7 

27 

11 

14 

117 

95.0 

16 

156.3 

24 

13 

16 

138 

84.5 

18 

157.3 

22 

14 

18 

149 

77.5 

20 

158.4 

20 

16 

20 

170 

70.4 

22 

158.9 

19 

17 

21 

181 

67.2 

228 


TABLE  49 


FOOTINGS 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 


2  TONS  ON  SOIL 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16,000 


Footing 
size 
b 

Column 
size 
a 
(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 
D 
(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
db.) 

(ft.) 

(in.) 

Square 

Round 

7 

0 

12 

175.1 

34 

H 

10 

12 

115 

139 

14 

177.6 

30 

12 

15 

138 

123 

16 

179.5 

27 

13 

17 

149 

110 

18 

181.3 

24 

14 

18 

161 

98 

20 

182.5 

22 

17 

21 

195 

90 

22 

183.1 

21 

17 

22 

195 

86 

24 

184.4 

19 

.    - 

20 

25 

230 

78 

7 

6 

12 

198.3 

38 

H 

11 

14 

136 

178 

14 

201.1 

34 

13 

16 

160 

160 

16 

203.9 

30 

15 

18 

185 

141 

18 

206.0 

27 

16 

21 

197 

127 

20 

207.4 

25 

. 

17 

22 

210 

117 

22 

208.8 

23 

19 

24 

234 

108 

24 

210.2 

21 

20 

26 

246 

99 

8 

0 

14 

226.4 

37 

M 

14 

17 

185 

198 

16 

229.6 

33 

16 

'       20 

211 

176 

18 

232.0 

30 

17 

22 

224 

160 

20 

233.6                28 

18    . 

23 

237 

149 

22 

235.2 

26 

20 

25 

264 

139 

24 

236.8 

24 

21 

27 

277 

128 

26 

238.4 

22 

23 

29 

303 

117 

8 

6 

14 

252.0 

41 

H 

14 

18 

196 

247 

16 

255.6 

37 

16 

21 

224 

223 

18 

259.2 

33 

19 

24 

267 

199 

20 

261.9 

30 

21 

26 

294 

181 

22 

263.7 

28 

22 

28 

309 

169 

24 

265.5 

26 

24 

30 

337 

156 

26 

267.3 

24 

25 

32 

351 

145 

9 

0 

16 

283.5 

40 

H 

11 

14 

256 

270 

18 

286.5 

37 

12 

16 

279 

250 

20 

289.5 

34 

14 

17 

325 

230 

22 

292.7 

31 

15 

19 

349 

209 

24 

294.4 

29 

16 

20 

372 

197 

26 

296.6 

27 

17 

22 

395 

182 

28 

298.7 

25 

19 

24 

442 

169 

9 

6 

16 

311.3 

44 

H 

12 

15 

295 

331 

18 

315.8 

40 

13 

17 

319 

301 

20 

319.3 

37 

14 

18 

344 

278 

22 

322.6 

34 

16 

20 

393 

256 

24 

326.0 

31 

17 

22 

418 

233 

26 

328.7 

29 

18 

23 

442 

218 

28 

330.6 

27 

20 

25 

491 

203 

229 


FOOTINGS 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 
2  TONS  ON  SOIL 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16,000 


TABLE  49 


Square  column. 


Footing 
size 
b 

Column 
size 
a 
vin.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 

(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
Ob.) 

(ft.) 

(in.) 

Square 

Round 

10 

0 

16                 340.0 

48 

% 

12 

16 

310 

400 

18 

346.3 

43 

14 

18 

362 

358 

20 

349.9                 40 

15 

19 

388 

334 

22 

353.8                 37 

17 

21 

440 

308 

24 

357.4                 34 

18 

23 

466 

284 

26 

360  .  0                 32 

19 

25 

492 

267 

28 

362.5 

30 

20 

26 

518 

250 

30 

365.0 

28 

22 

28 

565, 

233 

10 

6 

16 

369.3 

52 

H 

14 

17 

381 

478 

18 

376.1 

47 

15 

19 

408 

432 

20 

381.8 

43 

16 

21 

435 

395 

22 

386.0 

40 

. 

18 

23 

490 

367 

24 

390.0 

37 

19 

25 

517 

340 

26 

392.9 

35 

20 

26 

544 

321 

28 

395.5 

33 

21 

27 

571 

303 

30 

398.2 

31 

22 

28 

599 

285 

11 

0 

18 

406.9 

51 

H 

15 

19 

419 

514 

20 

414.5 

46 

17 

22 

486 

463 

22 

419.0 

43 

19 

24 

543 

433 

24 

423.5 

40 

20 

26 

572 

403 

26 

428.0 

37 

22 

28 

629 

373 

28 

431.0 

35 

23 

29 

658 

353 

30 

434.0 

33 

24 

31 

686 

333 

32 

437.2 

31 

26 

33 

743 

312 

34 

438.7 

30 

26 

33 

743 

302 

11 

0 

18 

439.7 

54 

H    • 

16 

21 

478 

595 

20 

446.3 

50 

18 

23 

538 

551 

22 

452.8 

46 

20 

25 

598 

507 

24 

457.8 

43 

21 

27 

628 

474 

26 

462.9 

40 

23 

29 

687 

441 

28 

466.3 

38 

24 

31 

717 

418 

30 

469.4 

36 

25 

32 

747 

397 

32 

472.7 

34 

26 

34 

111 

375 

34 

476.0 

32 

28 

35 

837 

353 

12 

0 

18 

471.4 

58 

H 

17 

22 

530 

697 

20 

480.5 

53 

19 

24 

593 

636 

22 

486.0 

50 

20 

26 

624 

600 

24 

493.2 

46 

22 

28 

686 

552 

26                 498.6 
28                 502  .  1 

43 
41 

24 
25 

31 
32 

748 
780 

516 
492 

30 

507.6 

38 

27 

35 

841 

456 

32 

511.1 

36 

28 

36 

873 

432 

34 

514.8 

34 

30 

38 

936 

408 

36 

518.4 

32 

31 

40 

967 

384 

230 


TABLE  50 


FOOTINGS 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 


3  TONS  ON  SOIL 


Punching  shear  =  120 
Bond  stress  =  100 
Tension  in  steel  =  16,6 


Footing 
size 
b 

Column 
size 

(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 

(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
Ub.) 

(ft.)    !   (in.) 

Square 

Round 

3 

0 

10 

52.4 

14 

H 

8 

10 

37.4 

10.5 

12 

52.5 

13 

8 

11 

37.4 

9.8 

14 

52.8 

11 

11 

14 

51.5 

8.3 

16 

52.9 

10 

12 

15 

56.1 

7.5 

3 

6 

10 

70.7 

18 

M 

7 

9 

38.7 

18.4 

12 

71.1 

16 

9 

11 

49.7 

16.3 

14 

71.4 

14 

10 

13 

55.2 

14.3 

16 

71.7 

12 

13 

16 

71.8 

12.3 

4 

0 

10 

91.4 

23 

M 

7 

9 

44.6 

30.7 

12 

92.2 

19 

10 

12 

63.7 

25.3 

14 

92.6 

17 

10 

13 

63.7 

22.7 

16 

93.0 

15 

12 

16 

76.5 

20.0 

18 

93.2 

14 

13 

17 

82.9 

18.7 

20 

93.4 

13 

14 

18 

89.2 

17.3 

4 

6 

10 

114.7 

27 

y* 

7 

9 

50.6 

45.6 

12 

115.7 

23 

9 

11 

65.0 

38.8 

14 

116.2 

21 

10 

13 

72.2 

35.5 

16 

116.9 

18 

12 

16 

86.7 

30.4 

18 

117.2 

17 

13 

16 

94.0 

28.7 

20 

117.7 

15 

15 

19 

108.0              25.3 

5 

0 

12 

141.2 

28 

H 

8 

11 

64  .  6              58  .  3 

14 

142.2 

25 

10 

12 

80.7     i          52    1 

J6 

143.1 

22 

12 

15 

97.0               45.8 

18 

143.7 

20 

13 

16 

105                   41.7 

20 

144.4 

18 

15 

19 

121                    37.5 

22 

145.0 

16 

16 

22 

129                   33.3 

5 

6 

12 

169.0 

33 

H 

8 

11 

71.4 

83.2 

14 

170.5 

29 

10 

12 

89.2 

73.1 

16 

172.0 

25 

13 

16 

116.0 

63  0 

18 

172.8 

23 

13 

17 

116 

58.0 

20 

173.6 

21 

15 

19 

134 

52   9 

22 

174.3 

19 

17 

21 

152 

47.9 

6             0 

12                 198.9 

38 

H 

8 

11 

78.2            114.0 

14                201.2 

33 

10 

12 

97.8     i         99.0 

16                202.5 

30 

11 

14 

108                  90  .  0 

18 

203.8 

27 

13 

16 

127 

81.0 

20 

205.2 

24 

15 

19 

147 

72.0 

22 

206.1 

22 

17 

21 

166 

66.0 

24 

207  .  0      . 

20 

19 

24 

186 

60.0 

26 

207.4 

19 

20 

25 

195 

57.0 

6             6 

12 

230.8 

43 

M 

9 

11 

95.7 

152.0 

14 

233.5 

38 

10 

12 

106 

134.0 

16 

235.6 

34 

11 

14 

117 

120.0 

18 

237.7 

30 

13 

17 

138 

106.0 

20 

238.7 

28 

14 

18 

149 

98.5 

22 

240.3 

25 

17 

21 

181 

88  0 

24 

241.4 

23 

18 

23 

192 

81.0 

26 

241.9 

22 

19 

24 

202 

77.4 

231 


FOOTINGS 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16,0 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 
3  TONS  ON  SOIL 


Footing 
size 

Column 

Allowable 
i  -_  j 

Total 

Steel 

Volume 

b 

size 
a 
(in.) 

load 
P 

(thousands 
of  uounds) 

depth 
(in.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 

of 
concrete 
(cu.  ft.) 

(ft.) 

(in.) 

Square 

Round 

db.) 

7 

0 

14                 267.7 

43 

H 

11 

14 

121                  176 

16                 270.2 

39 

12 

15 

138                  159 

18                 272.6 

35 

13 

16 

149                  143 

20                 275.0 

31 

15 

19 

172 

126 

22 

276.3 

29 

16 

20 

184 

118 

24 

277.5 

27 

18 

22 

207 

110 

26 

278.7 

25 

19 

24 

218 

102 

28 

279.9 

23 

21 

27 

241 

94 

7             6 

14 

303.7 

48 

y* 

12 

.15 

148 

225 

16 

307.4 

43 

13 

16 

160 

202 

18 

310.0 

39 

14 

18 

173 

183 

20 

312.9 

35 

16 

20 

197 

164 

22 

315.0 

32 

17 

22 

210 

150 

24 

316.3 

30 

18 

22 

222 

141 

26 

317.8 

28 

19 

24 

234 

131 

28 

319.2 

26 

21 

27 

257 

122 

8 

0 

16 

345.6 

48 

H 

14 

17 

185 

256 

18                 349.6 

43 

15 

19 

198 

229 

20 

352.8 

39 

17 

21    .              224 

208 

22 

.     355.2 

36 

18 

23                 237                  192 

24 

357.6 

33 

20 

25                 264                  176 

26 

359  .  2 

31 

21 

26                 277                 165 

28 

360.7 

29 

21 

27         •!       277                 155 

30 

362.4 

27 

23 

29 

303 

144 

8 

6 

16 

386.6 

53 

y* 

15 

19 

211 

319 

18 

390.1 

48 

16 

21 

224 

289 

20 

393.7 

44 

18 

22   ' 

252 

265 

22                 397.3 

40 

19 

24 

266 

241 

24                 400  .  1 

37 

21 

27 

294 

223 

26 

401.9 

35 

22 

28 

309 

211 

28 

404.5 

32 

24 

30 

337 

193 

- 

30 

406.3 

30 

25 

32 

351 

181 

9 

0 

18 

432.2 

53 

y% 

.11 

14 

256 

358 

20 

437.3 

48 

12 

15 

279 

324 

22 

441.4 

44 

13 

17 

302 

297 

24 

444.4 

41 

14 

18 

325 

277 

26 

447.4 

38 

15 

20 

349 

257 

28 

449.5 

36 

16 

21 

372 

243 

30 

452.5 

33 

18 

23 

418 

223 

32 

454.6 

31 

20 

25 

465 

209 

34 

456.6 

29 

21 

27 

488 

196 

9 

6 

18 

476.1 

58 

H 

12 

15 

295 

436 

20 

481.6 

53 

13 

16 

319 

399 

22 

486.1 

49 

14 

18 

344 

369 

24 

490.6 

45 

15 

19 

369 

339 

26 

494.1 

42 

16 

21 

393 

316 

28 

497.5 

39 

17 

22 

418 

293 

.-30                 499.8                 37 

18 

23 

442 

278 

32                 502  .  0                 35 

19 

24 

467 

263 

34                 504.3                 33 

20 

26 

492 

248 

232 


TABLE  50 


FOOTINGS 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 
3  TONS  ON  SOIL 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16, 000 


Footing 
size 
6 

Column 
size 
a 
(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 

(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
Ob.) 

(ft.) 

(in.) 

Square 

Round 

10 

0 

18 

521.3 

63 

H 

13 

16 

336                525 

20 

527.5 

58 

14 

17 

362                 483 

22 

533.7 

53 

15 

19 

388                442 

24 

538.9 

49 

16 

20 

414                 408 

26 

542.5 

46 

17 

22 

440                383 

28 

546.3 

43 

18 

23 

465                 358 

30 

550.0 

40 

19 

25 

492                333 

32 

552.5 

38 

20 

25 

518                317 

34 

555.0 

36 

21 

27 

544                 300 

36 

557.5 

34 

22 

28                 569                 283 

10 

6 

18 

566.3 

69 

K 

14 

17 

381                 634 

20 

574.5 

63 

15 

18 

408       ,          579 

22 

581.5 

58 

16 

20 

435                 533 

24            .     587.1 

54 

17 

21 

463                496 

26                 593  .  2 

50 

18 

23 

490                456 

28                 596  .  6 

47 

19 

24 

517                432 

30                 600.8 

44 

20 

26 

544                 404 

32                 604  .  9 

41 

22                   28 

599                 377 

34                 608  .  8 

39 

23 

29 

626                358 

36                 610.5 

37 

23 

30 

626                340 

38                 613.2 

35 

24 

31 

653                 322 

11 

0 

20                 623.2 

68 

M 

15 

20 

458                 686 

22                 630  .  8 

63 

17 

21 

486                 635 

24                 638  .  3 

58 

18 

22 

515 

585 

26                 644.4 

54 

19 

24 

543 

544 

28 

648.9 

51 

20 

25 

582 

514 

30 

653.4 

48 

21 

27 

600 

484 

32 

657.9 

45 

23 

29 

658 

454 

34 

662.5 

42 

24 

31 

686 

423 

36 

665  .5 

40 

25 

32 

715 

403 

38 

668.5 

38 

26 

33 

743 

383 

40 

671.5 

36 

27 

34 

772 

363 

11 

6 

20 

672.9 

73 

H 

16 

21 

478 

804 

22 

682.8 

67 

18 

23 

538 

738 

24 

689.5 

63 

19 

24 

568 

694 

26                 696.0 

59 

20 

25 

598 

650 

28                 702  .  6 

55 

21 

27 

628 

606 

30                 709  .  1 

51 

23 

29 

687 

562 

32                 714.1 

48 

24 

31 

717 

529 

34                 717.5 

46 

25 

32 

747 

507 

36                 722.3 

43 

26 

34 

777 

474 

38                 725  .  7 

41 

27 

35 

807 

452 

40                 729  .  1 

39 

28 

36 

837 

429 

42                 732.3 

37 

29 

37 

866 

408 

12             0 

22                 734.4 

72 

M 

19 

24 

593 

864 

24 

743.4 

67 

20 

25 

614 

804 

26 

750  .  6                63 

21 

27 

655 

756 

28 

757  .  8                59 

22 

28 

686 

708 

30 

765.0                55 

24 

31 

748 

660 

32 

770.4                52 

25 

32 

780 

624 

34 

775.8                49 

27 

34 

842 

588 

36 

779.4                47 

27 

35 

842 

564 

38                 784.8                44 

29 

37 

904 

528 

40                 788  .  4                42 

30 

38 

936 

504 

42                 792  .  0                40 

31 

39 

967 

480 

44                 793.8 

39 

31 

39 

967 

468 

233 


FOOTINGS 


•Square  column 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 

A  J  

I            ^ 

4  TONS  ON  SOIL 
Punching  shear  =  120                                                                                            m  Iff 

I 

Bond  stress         =100                                                                                               HfH 

Q   •* 

Tension  in  steel  -  16,000                                                                                          ±5  gFi 

1 

Footing 
size 
b 

Column 
size 
a 
(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 
D 

(in.) 

Steel 

Volume 

of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
Ob.) 

(ft.) 

(in.) 

Square 

Round 

3 

0 

10 

70.0                 18 

H                      7                      9                    32.8               13.5 

70.3                 15 

9                    11                   42.0               11.3 

14                    70.5                 13 

10                   13                  46.7                9.8 

16                   70.6                 12 

11 

14 

51.5                 9.0 

18                   70.8                  11 

12 

15 

56.1                 8.3 

3 

6               10 

94  .  5                 23 

M 

7                     9 

38.7               23.5 

12 

94.9                 20 

8 

10 

44.2               20   4 

14 

95.4                 17 

10 

12 

55.2               17.4 

16 

95.7                 15 

11 

15 

60.7               15.3 

18 

95.9                  14 

12                   15 

66.3               14.3 

20                   96.2              '    12 

15 

19 

82.9               12.3 

4              0 

10 

122.2                 29 

H 

7 

9 

44  .  6               38   7 

12 

123.0                 25 

8 

10 

51.0               33  .  3 

14 

123.8 

21 

10 

12 

63.7 

28.0 

16 

124.1 

19 

11 

14 

70.1 

25.3 

18 

124.6  ' 

17 

13 

16 

82.9 

22.7 

20 

125.0 

15 

15 

19 

95.6 

20.0 

22 

125.3 

14 

15 

19 

95.6 

18.7 

4 

6 

10 

153.1 

35 

H 

7 

9 

50  .  6               59  .  0 

12 

154.4 

30 

8 

10 

57  .  7               50  .  6 

14 

155.4 

26 

10 

12 

72  .  2          .     43  .  8 

1 

16 

156.2 

23 

11 

14 

79.5 

38.8 

1 

18 

156.7 

21 

12 

15 

86.7 

35.4 

20 

157.2 

19 

14 

17 

101.0 

32.0 

22 

157.7 

17 

16 

20 

116.0               28.7 

5 

0 

12 

188.7 

36 

M 

8 

11 

64.6 

75.0 

14 

190.3 

31 

10 

12 

80.7 

64.6 

16 

191.6 

27 

11 

14 

88.8 

56.2 

18 

192.2 

25 

12 

15 

97.0 

52.1 

20 

193  .  1 

22 

14 

18 

113 

45.8 

22 

193.7 

20 

16 

20 

129 

41.7 

24 

194.1 

19 

17 

21 

137 

39.6 

5 

6 

12 

226.1 

42 

H 

9 

11 

80.2 

106.0 

14 

228.0 

37 

10 

12 

89.2 

93.2 

16 

229.9 

32 

11 

14 

98.2 

80.7 

18 

231  .0 

29 

13 

16 

116 

73.1 

20 

232.2 

26 

14 

18 

125 

65.5 

22 

232.9 

24 

15 

19 

134 

60.5 

24 

233  .  7 

22 

17 

22 

152 

55.4 

26 

234.4 

20 

19 

24 

170 

50.4 

6 

0 

14 

268.6 

43 

H 

9 

12 

88.0 

129.0 

16                 270.6 

38 

11 

14 

108 

116.0 

18                 272.7 

34 

12 

16 

117 

102.0 

20                 274.0 

31 

14 

17 

137 

93.0 

22                 275  .  4 

28 

15 

19 

147 

84.0 

24                 276.3 

26 

17 

21 

166 

78.0 

26 

277.2 

24 

18 

23 

176 

72.0 

28 

278.1 

22 

20 

26 

195 

66.0 

6 

6 

14 

312.1 

49 

y* 

10 

13 

106 

172.0 

16 

314.7 

44 

11 

14 

117 

155.0 

18 

317.5 

39 

13 

16 

138 

137.0 

20 

319.5 

35 

14 

18 

149 

123.0 

22 

321.1 

32 

15 

19 

160 

112.0 

24 

322.2 

30 

17 

21 

181 

106.0 

26 

323  .  2 

28 

18 

23 

192 

98.5 

28 

,",  >  1  :  .  3 

26 

i/ 

19 

25 

202 

91  .5 

30 

325  .  3 

24 

21                   27 

223 

•   84.5 

234 


TABLE  51 


FOOTINGS 


5quar<s  column . 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 


4  TONS  ON  SOIL 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16,0 


Footing 
size 

i 

Column 
size 
a 
(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 

(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
db.) 

(ft.) 

(in.) 

Square 

Round 

7 

0 

16 

361.4 

50 

H 

12 

15 

138 

204 

18 

364.4 

45 

13 

16 

149 

184 

20 

367.5 

40 

14 

18 

161 

163 

22 

369.3 

37 

15 

19 

172 

151 

24 

371.1 

34 

17 

21 

195 

139 

26 

372.4 

32 

18 

22 

207 

131 

28 

374.2 

29 

20 

25 

230 

118 

30 

375.4 

27 

22 

27 

252 

110 

32 

376.7 

25 

25 

30 

287 

102 

7 

6              16 

410.6 

55 

H 

13 

16 

160 

263 

18 

414.2 

51 

14 

17 

173 

239 

20 

417.7 

46 

15 

19 

185 

215 

22 

420.4 

42 

16 

20                 197 

197 

24 

422.5 

39 

16 

21                 197 

183 

26 

424.7 

36 

18 

22                 222 

168 

28 

426.8 

33 

20 

25 

246 

155 

30 

428.2 

31 

21 

27 

259 

145 

32 

429.6 

29 

23 

29 

284 

136 

34 

431.0 

27 

25 

31 

308 

126 

8 

0               18 

466.4 

57 

H 

15 

19 

198 

304 

20 

471.2 

51 

16 

21 

211 

272 

22 

474.3 

47 

17 

22 

224 

251 

24 

477.6 

43 

18 

23 

237 

229 

26 

480.0 

40 

19 

24 

250 

213 

28 

482.4 

37 

20 

25 

264 

197 

30 

484.0 

35 

21 

26 

277 

187    ' 

32 

485.6 

33 

22 

28 

290 

176 

34 

487.2 

31 

24 

30 

316 

165 

36 

488.8 

29 

26 

32 

343 

155 

8 

6 

18 

521.0 

63 

H 

16 

20 

224 

380 

20 

526.5 

57 

17 

22 

238 

343 

22 

531.0                52 

19 

24 

266 

313 

24 

534  .  6                48 

20 

25 

281 

289 

26 

537.3                45 

21 

26 

294 

271 

28 

540.0                42 

21 

27 

294 

253 

30 

542  .  7                39 

22 

28 

309 

235 

32 

545.4               .36 

24 

31 

337 

217 

34 

557.2 

34 

25 

31 

351 

205 

36 

549.0 

32 

26 

33 

365 

193 

9 

0 

20 

584.2 

63 

K 

12 

15 

279 

425 

22 

589.4 

58 

13 

16 

302 

391 

24 

593.3 

54 

13 

17 

302                 364 

26 

598.3 

49 

15 

19 

349 

331 

28 

601.4 

46 

16 

20 

372 

310 

50 

604.4 

43 

17 

21 

395 

290 

32 

607.5 

40 

18 

23 

418                 270 

34 

609.6 

38 

19 

24 

442                 256 

36 

611.5 

36 

20 

26 

465                 243 

38 

613.6 

34 

22 

28 

511                 229 

9 

6              20 

644.1 

69 

H 

13 

16 

319                 519 

22 

649.9 

64 

14 

18 

344                 481 

24 

655.5 

59 

14 

18 

344                 443 

26 

660.0 

55 

15 

19 

369                 413 

28 

664.5 

51 

16 

20 

393                383 

30 

667.8 

48 

16 

21 

393                361 

32 

671.3 

45 

17 

22 

418         '       338 

34 

674.6 

42 

19  .                24 

467                316 

36 

676.8 

40 

20                  26 

491                 301 

38 

679.1 

38 

21                   27 

516 

286 

40                681.3 

36 

23                    29                 565 

271 

235 


FOOTINGS 


TABLE  51 


DESIGN  OF  SINGLE  SQUARE  FOOTINGS 


Punching  shear  =  120 
Bond  stress  =100 
Tension  in  steel  =  16, 000 


4  TONS  ON  SOIL 


Footing 
size 
b 

Column 
size 
a 
(in.) 

Allowable 
load 
P 
(thousands 
of  pounds) 

Total 
depth 

(in.) 

Steel 

Volume 
of 
concrete 
(cu.  ft.) 

Size 
(in.) 

No.  rods  each  way 

Weight  of 
sq.  rods 
Ob.) 

(ft.) 

(in.) 

Square 

Round 

10 

0 

22                 712.5 

70                   H 

15 

19 

388                 583 

24                718.8 

65 

15 

19 

388 

541 

26                725.0 

60 

17 

21 

440- 

500 

28                730  .  0 

56 

17 

22 

440 

467 

30                735.0 

52 

18 

23 

466 

4  33 

32                 738.8 

49 

19 

24 

492 

408 

34                742.5 

46 

20 

25 

518 

383 

36                745.0 

44 

20 

25 

518                 367 

38                748.7 

41 

22 

28 

569                 342 

40                751.2 

39 

23 

29 

595 

325 

42                 753.8                 37 

24 

31 

620                 308 

10             6 

22                777.3                 76 

H 

16 

20                 435                 698 

j 

24                 785  .  5                 70 

17                    21                 462          i        643 

26                 792.5                 65 

18                    22 

490        .         597 

| 

28                797.9                61 

18 

23 

490                 561 

30 

803.3                57 

19 

24                 517                 524 

1 

32 

807  .  7                54 

20 

25 

544                 496 

| 

34 

811.6 

51 

20 

26                 544                 469 

36 

815.9 

48 

21 

27                 571                  441 

38 

820.0 

45 

'23 

29 

626                 413 

40 

822.7 

43 

23 

29 

626                 395 

42 

825.4 

41 

24 

31 

663 

377 

44 

828.3 

39 

25 

32 

680 

358 

1                       r 

11              0 

24 

853.0                 76                   y* 

18 

22 

515 

766 

• 

26 

860.6                71 

19 

24 

543 

716 

|    . 

28 

868.2                 66 

20 

25 

572 

665 

30 

874  .  2                62 

21 

26 

600 

625 

32                 880.2                 58 

21 

27 

600 

585 

34                 884  .  8                 55 

22 

28 

629 

554 

36                 889.4                 52 

23 

29 

658 

524 

i 

38                 893  .  8                49 

24 

30 

686 

494 

i 

40                 896.8                 47 

24 

31 

686 

474 

42 

900.0 

45 

25 

32 

715 

453 

44 

903  .  0 

43 

25 

32 

715 

433 

46 

906.0 

41 

26 

33 

743 

413 

11              6 

24                 922.4 

82                    H                    19 

24 

568 

903 

26                931.0 

77 

20 

25 

598 

848 

28                 940.8 

71 

21 

27 

628 

782 

30 

947.4                67 

22 

28 

657 

738 

32 

954.0 

63 

23 

29 

687 

694 

34 

958.9 

60 

23 

30 

687 

661 

36 

963.8 

57 

24 

30 

717 

628 

38 

968.8 

54 

25 

31 

747 

595 

40 

973.7 

51 

26 

33 

777 

562 

42 

977.0 

49 

26 

33 

777 

540 

44 

982.0 

46 

28 

35 

837 

507 

46 

985.2 

44 

29 

36 

866 

485 

48 

988.7 

42 

29 

37 

866 

462 

12             0 

26 

1002  .  7 

83                    H 

21 

26 

655 

996 

28 

1013.3 

77 

22 

28 

686 

925 

30 

1022.2 

72 

23 

29 

717 

865 

32 

1029.6 

68 

24 

30 

748 

816 

34 

1036.8 

64 

25 

32 

780 

768 

36 

1042.3 

61 

26 

32 

811 

732 

38 

1047.5 

58 

26 

34                 811 

697 

40 

1053.0 

55 

27 

35 

842 

660 

42 

1058.4 

52 

29 

36 

905 

624 

44 

1062.0 

50 

29 

37                 905 

600 

46 

1065.6                 48 

30 

38                 936 

576 

48 

1069.2                 *6 

30 

39 

936 

552 

50 

1073  .  8                 44 

31 

40 

967 

528 

236 


SECTION  10 
MISCELLANEOUS 

Estimates. — Estimates  of  the  cost  of  the  concrete  work  for  buildings  and  similar 
structures  can  be  easily  made  by  applying  current  unit  costs  to  the  quantities  ob- 
tained from  the  tables  and  diagrams. 

Diagram  66  gives  the  quantities  of  concrete,  steel  and  forms  for  typical  square 
panels  of  a  three  beam*  and  girder  floor  system.  Although  the  quantities  of  steel  or 
concrete  may  be  somewhat  affected  by  changing  the  proportions  of  beams  or  girders, 
the  total  cost  will  vary  only  slightly.  Quantities  for  flat  slab  floors  may  be  found  in 
Section  2. 

By  means  of  Diagrams  42  and  43  of  Section  7,  which  give  weights  of  floor  panels, 
the  column  and  footing  loads  can  be  quickly  estimated  and  the  quantities  taken  from 
the  column  and  footing  tables. 

Loads. — Tables  52,  53  and  54,  give  the  building  code  requirements  for  live  load, 
weights  of  contents  of  storage  warehouses,  and  weights  of  building  materials 
respectively. 


237 


MISCELLANEOUS 


DIAGRAM  66 


APPROXIMATE  QUANTITIES  OF  CONCRETE,  STEEL  AND  FORMS  FOR 

TYPICAL  SQUARE  INTERIOR  PANELS  OF  THREE  BEAM  AND  GIRDER 

FLOOR  SYSTEM  DESIGNED  IN  ACCORDANCE  WITH  JOINT 

fc=650  COMMITTEE  RECOMMENDATIONS 

fs  =16*000  (COLUMNS  NOT  INCLUDED) 


4.  4.014 -DC  aad     cpuno 


o       o»        oo       r:       <o       10 
o       ol       o        ol       c> 


238 


TABLE  52 


MISCELLANEOUS 


BUILDING  CODE  REQUIREMENTS  FOR  LIVE  LOAD 


• 
Structure 

i 

Boston 

Buffalo 

Chicago 

Cincinnati 

Indianapolis 

Milwaukee 

Minneapolis 

! 

1 

New  York 

Philadelphia 

Pittsburgh 

.2 
1 

£ 

San  Francisco 

A 

1 

Washington 

\partments     

60 

50 

70 

40 

40 

50 

30 

50 

40 

70 

50 

60 

40 

50 

100 

100 

70 

75 

100 

100 

100 

125 

125 

100 

120 

150 

100 

Fxd  seat  auditoriums 

75 

100 

50 

75 

75 

Mov.  seat  auditoriums  
Churches             

125 

100 

100 

1?5 

80 
50 

75 

125 

100 
75 

Dance  halls            

?00 

100 

150 

100 

150 

100 

200 

100 

150 

250 

Theaters 

100 

100 

100 

125 

50 

100 

75 

75 

Theater  balconies  
Theater  stairways     

80 

100 

Dwellings   

60 

50 

40 

40 

40 

50 

30 

50 

40 

40 

70 

70 

50 

60 

40 

50 

Hospitals         

70 

50 

50 

30 

50 

70 

50 

60 

50 

Hotels 

60 

70 

50 

40 

75 

30 

50 

40 

70 

50 

60 

40 

50 

First  floors 

100 

100 

75 

Corridors 

125 

100 

75 

Office  rooms 

50 

75 

Manufacturing          ........ 

175 

150 

?00 

150 

200 

150 

250 

Light  manufacturing  
Mercantile  

125 

m 

125 

?50 

120 

100 
100 

100 

100 

100 

100 

125 
?00 

120 

100 
150 

125 

125 

Retail  stores  
Heavy  storehouses 

125 
250 

125 
250 

120 

100 

100 
150 

100 
200 

100 

100 

125 

120 

120 
150 

150 

125 

250 

125 

110 
150 

Warehouses                    .  . 

250 

150 

150 

?00 

200 

150 

200 

150 

250 

150 

Offices     

75 

100 

70 

50 

50 

75 

40 

75 

70 

60 

100 

60 

60 

50 

75 

First  floor  

150 

100 

150 

80 

100 

100 

125 

Corridors  

100 

110 

100 

125 

100 

110 

Schools  —  class  rooms 

75 

60 

60 

100 

40 

100 

60 

75 

75 

50 

75 

Assembly  rooms            .... 

125 

100 

75 

60 

125 

75 

Corridors            

60 

125 

100 

Stairways   

60 

Sidewalks  

?00 

300 

300 

150 

300 

300 

300 

150 

Stables,      carriage      houses, 
garages 

100 

120 

100 

75 

85 

80 

85 

100 

75 

75 

Stairways,  general 

70 

100 

80 

60 

70 

100 

Fire  escapes   .  .  . 

70 

70 

100 

Roofs  —  slope  under  20°  
Over  20°  (hor.  proj.)  
Wind  pressures  

30 

40 

40 
30 

25 
20 

25 
20 

30 

30 
30 

50 
50 
30 

30 

40 
30 

30 
30 
30 

50 

30 
30 

30 
20 
20 

40 
40 

25 
25 
30 

239 


TABLE  S3 


MISCELLANEOUS 


CONTENTS  OF  STORAGE  WAREHOUSES 


Material 

Pounds 

cubic  foot 
of  space 

Height 
of  pile, 
feet 

Pounds 
per 
square  foot 
of  floor 

Recommended 
live  loads, 
pounds  per 
square  foot 

Produce,  Grain,  Fruit,  Etc. 
Grain,  in  bulk 
Barley  and  corn 

37 

8 

296         * 

Oats  

26 

8 

208 

Rye  and  wheat 

48 

8 

384 

Fruit  and  vegetables,  in  bulk  

Apples,  pears,  etc       .        .  . 

38 

8 

304 

Potatoes,  turnips,  etc  
Miscellaneous  produce,  packed 
Beans,  in  bags                                .... 

44 
40 

8 
8 

352 
320 

Corn,  in  bags  

31 

8 

248 

250  to  300 

Cornmeal,  in  barrels  

37 
26 

6H 

240 
234 

Rice,  in  bags  
Wheat,  in  bags 

58 
39 

5 

8 

290 
312 

Wheat  flour,  in  barrels  
Hay,  in  bales,  not  compressed  
Hay,  in  bales,  compressed  
Straw,  in  bales,  compressed  

Groceries 

Miscellaneous  articles,  packed  

40 
14 
24 
19 

7 
9 
9 
9 

280 
126 
216 
171 

Butter,  lard,  etc.,  in  carrels  
Canned  goods,  preserves,  etc.,  in  cases.  . 
Cheese  

32 
58 
30 

6 
6 

8    '-- 

192 
348 
240 

Coffee,  green,  in  bags                 

39 

8 

312 

Coffee,  roasted,  in  bags  

33 

8 

264 

Dates  and  figs,  in  cases,  average  
Meat,  beef,  pork*  etc.,  in  barrels  
Molasses,  in  barrels  
Salt,  finely  ground  in  sacks 

65 
37 
48 
60 

5 
5 
5 
5 

325 
185 
240 
300 

250  to  300 

Soap  powder,  in  cases  
Starch,  in  barrels 

38 
25 

8 
7 

288 
175 

Sugar,  in  barrels  

43 

5 

215 

Tea,  in  chests  
Wines,  liquors,  etc.,  in  barrels  

Dry  Goods,  Cotton,  Wool,  Etc. 
Cotton,  in  bales,  compressed,  average.  .  .  . 
Cotton,  unbleached  goods,  in  bales  
Cotton,  tickings  and  duck,  in  bales  
Cotton,  printed  goods,  in  bales  

25 

48 

25 
24 
35 

19 

8 
5 

9 
9 
8 
9 

200 
240 

225 
216 
280 
171 

Cotton,  printed  goods,  in  cases  
Cotton,  quilts  and  flannels,  in  cases 

31 
16 

8 
9 

248 
144 

Cotton,  yarn,  in  cases  
Hemp,  in  bales,  compressed  
Hemp,  manila,  in  bales,  compressed  
Hemp,  sisal,  in  bales,  compressed  
Hemp,   tow,  in  bales,  compressed.  
Hemp,  burlaps,  in  bales,  compressed  

25 
22 
26 
24 
29 
43 
41 

8 
8 
9 
9 
9 
6 
6 

200 
176 
234 
216 
261 
258 
246 

200  to  250 

Linen,  bleached  goods,  in  cases  

35 

7 

245 

Linen,  damask  goods,  in  cases                .  . 

50 

5 

250 

Wool,  in  bales,  not  compressed  

13 

9 

117 

Wool,  in  bales,  compressed  
Wool,  dress  goods,  flannels,  in  cases  
Wool,  worsted  goods,  in  cases  

48 
18 
27 

5 
9 
9 

240 
162 
243 

19 

9 

171 

Excelsior,  in  bales,  compressed  

19 

9 

171 

240 


TABLE  63 


MISCELLANEOUS 


CONTENTS  OF  STORAGE  WAREHOUSES 


Material 

Pounds 
per 
cubic  foot 
of  space 

Height 
of  pile, 
feet 

Pounds 
per 
square  foot 
of  floor 

Recommended 
live  loads, 
pounds  per 
square  foot 

Drugs,  Oils,  Paints,  Etc. 
Chemicals: 
Acids,  muriatic  and  nitric,  in  carboys.  .  . 
Acids,  sulphuric,  in  carbovs.  .  . 

45 
60 

m 

75 
100 

Ammonia,  in  carboys  .    . 

30 

1?1 

50 

Alum,  pearl  alum,  in  barrels  
Bleaching  powder,  in  hogsheads  
Copper  sulphate,  blue  vitriol,  in  bbls.  .  . 
Soda,  caustic  soda,  in  iron  drums  
Soda,  soda  ash,  in  hogsheads  

33 
31 
45 

88 
62 

7 

I* 
$ 

231 
103 
225 
294 
170 

Soda  crystals,  sal  soda,  in  barrels  
Soda  nitrate,  niter,  in  barrels  
Soda  silicate,  in  barrels  

30 
45 
53 

5 
5 
5 

150 
225 
265 

Zinc  sulphate,  white  vitriol,  in  barrels  .  . 
Oils,  fats,  resins,  etc.: 
Glycerine,  in  cases  

40 
52 

5 

6 

200 
312 

Oils,  animal,  lard,  etc.,  in  barrels.  .  . 

34 

6 

204 

200  to  250 

Oils,  vegetable,  linseed,  in  barrels  
Oils,  mineral,  lubricants,  in  barrels.  .  .  . 
Oils,  petroleum,  kerosene,  in  barrels.  .  .  . 
Oils,  naphtha,  gasolene,  in  barrels  
Rosin,  in  barrels           

36 
35 
33 

28 
48 

6 
6 
6 
6 

216 
210 
198 
168 
288 

Shellac  gum    in  boxes  .       . 

38 

& 

228 

Tallow,  in  barrels  

37 

g 

222 

Dye  stuffs,  paints,  etc.: 

43 

6 

258 

Logwood  extract,  in  boxes  

70 

4H 

315 

Sumac,  in  boxes 

39 

5 

195 

Red  lead,  litharge,  dry,  in  barrels  
White  lead,  dry  in  barrels 

132 
86 

3% 
4% 

495 
409 

White  lead,  paste,  in  cans  

Building  Materials 
Cement,  natural,  in  barrels  

174 
59 

3>I 
6 

609    • 
354 

) 

Cement,  Portland,  in  barrels  
Lime,  quick  lime,  ground,  in  barrels.  .  .  . 

73 
50 

6 
5 

438 
250 

300  to  400 

Plaster  of  Paris,  ground,  in  barrels.    . 

53 

5 

265 

1 

Sheet  Metal  and  Wire 
Sheet  tin,  in  boxes 

278 

1  LZ 

417 

Wire,  insulated  copper,  in  coils 

63 

5 

315 

Wire,  galvanized  iron  in  coils 

74 

414 

333 

300  to  400 

Wire,  magnet  wire,  on  spools.  .  .  . 

75 

g 

450 

Miscellaneous 
Chinawarc,  glassware,  in  crates 

40 

g 

320 

Chinaware,  glassware,  in  casks  ..... 

14 

g 

126 

Glass,  in  boxes  

69 

g 

360 

Hardware,  door  and  sash  checks,  in  cases. 
Hardware,  hinges,  in  cases.    .'.. 

46 

64 

6 

g 

276 
384 

Hardware,  locks,  in  cases  

31 

6 

186 

Hardware,  screws,  in  boxes  
Hides,  raw,  not  compressed,  in  bales  
Hides,  raw,  conipressed,  in  bales  
Leather  in  bales 

101 
13 
23 
16 

4 
10 
10 
10 

404 
130 
230 
160 

300  to  400 

Paper,  calendered  paper  \  
Paper,  newspaper,  manila,  strawboards.  .  . 
Paper  writing  paper 

50 
35 

64 

6 
6 
g 

300 
210 
384 

Rope  in  coils  

42 

g 

252 

241 


MISCELLANEOUS 


TABLE  54 


WEIGHTS  OF  BUILDING  MATERIALS 


Kind 


Weight  in  Ib. 
per  sq.  ft. 


FLOORS 
.  maple  finish  floor  and  %-in.  spruce  under  floor  on  2  X  4-in.  sleepers,  16-in.  centers,  with 

2-in.  dry  cinder  concrete  filling 

Cinder  concrete  filling  per  inch  of  thickness 

Cement  finish  per  inch  of  thickness • 

Asphalt  mastic  flooring  IJ-^  in.  thick 

3-in.  creosoted  wood  blocks  on  H-in.  mortar  base 

Solid  flat  tile  on  1-in.  mortar  bed 

CEILINGS 

Plaster  on  tile  or  concrete 

Suspended  metal  lath  and  plaster 

ROOFS 

Five-ply  felt  and  gravel 

Four-ply  felt  and  gravel 

Three-ply  ready  roofing 

Cement  tile 

Slate,  \i  in.  thick 

Sheathing,  1  in.  thick,  yellow  pine 

2-in.  book  tile 

3-in.  book  tile 

Skylight  with  galvanized  iron  frame,  2s~in-  glass 


18 
7 
12 
18 
21 


1 
16 

J* 

12 
20 


Kind 

Weight  in  Ib.  per  sq.  ft. 

Unplastered 

One  side 
plastered 

Both  sides 
plastered 

WALLS 
9-in.  brick  wall 

84 
121 
168 
205 
243 
60 
75 
102 
33 
45 

17 
18 
25 
31 
35 
10 
12 
14 
16 

89 
126 
173 
210 
248 
65 
80 
107 
38 
50 

22 
23 
30 
36 
40 
15 
17 
19 
21 

43 
55 

27 
28 
35 
41 
45 
20 
22 
24 
26 
20 
32 
22 

13-in.  brick  wall  

18-in.  brick  wall  
22-in.  brick  wall  

26-in.  brick  wall  
4-in  brick  4-in  tile  backing 

4-in.  brick,  8-in.  tile  backing  
9-in.  brick,  4-in.  tile  backing  
8-in.  tile  

12-in.  tile                               

PARTITIONS 
3-in.  clay  tile  
4-in.  clay  tile  
6-in.  clay  tile  

8-in.  clay  tile  
10-in.  clay  tile. 

3-in.  gypsum  block  
4-in.  gypsum  block  

6-in.  gypsum  block  
2-in.  solid  plaster  
4-in.  solid  plaster  
4-in.  hollow  plaster  

Kind 

Weight  in  Ib. 
per  cu.  ft. 

Kind 

Weight  in  Ib. 
per  cu.  ft. 

Beech  
Birch  
Brickwork  
Concrete,  cinder,  structural 

42 
42 
120 
108 

Limestone  
Maple  
Marble  
Oak 

150 
42 
168 
48 

Concrete,  cinder,  floor  filling  
Concrete,  stone  
Concrete,  stone,  reinforced  
Douglas  fir  .  

96 
144 
150 
36 

Pine,  southern  yellow  
Sandstone  
Spruce  

42 
144 
30 

Granite  
Granolithic  surface  

168 
144 

unfilled  

72 
120 

242 


APPENDIX 
RULINGS  PERTAINING  TO  DESIGN  AND  WORKING  STRESSES 


Joint  Committee  Recommendations* 
Design 

Massive  Concrete. — In  the  design  of  massive  or  plain  concrete,  no  account  should 
be  taken  of  the  tensile  strength  of  the  material,  and  sections  should  usually  be  proportioned 
so  as  to  avoid  tensile  stresses  except  in  slight  amounts  to  resist  indirect  stresses.  This  will 
generally  be  accomplished  in  the  case  of  rectangular  shapes  if  the  line  of  pressure  is  kept 
within  the  middle  third  of  the  section,  but  in  very  large  structures,  such  as  high  masonry 
dams,  a  more  exact  analysis  may  be  required.  Structures  of  massive  concrete  are  able  to 
resist  unbalanced  lateral  forces  by  reason  of  their  weight;  hence  the  element  of  weight 
rather  than  strength  often  determines  the  design.  A  leaner  and  relatively  cheap  concrete, 
therefore,  will  often  be  suitable  for  massive  concrete  structures. 

It  is  desirable  generally  to  provide  joints  at  intervals  to  localize  the  effect  of  contraction. 

Massive  concrete  is  suitable  for  dams,  retaining  walls,  and  piers  in  which  the  ratio 
of  length  to  least  width  is  relatively  small.  Under  ordinary  conditions  this  ratio  should 
not  exceed  four.  It  is  also  suitable  for  arches  of  moderate  span. 

Reinforced  Concrete. — The  use  of  metal  reinforcement  is  particularly  advantageous 
in  members  such  as  beams  in  which  both  tension  and  compression  exist,  and  in  columns 
where  the  principal  stresses  are  compressive  and  where  there  also  may  be  cross-bending. 
Therefore,  the  theory  of  design  here  presented  relates  mainly  to  the  analysis  of  beams  and 
columns. 

General  Assumptions,     (a)  Loads. — The  forces  to  be  resisted  are  those  due  to: 

1.  The  dead  load,  which  includes  the  weight  of  the  structure  and  fixed  loads  and  forces. 

2.  The  live  load,  or  the  loads  and  forces  which  are  variable.     The  dynamic  effect  of 
the  live  load  will  often   require  consideration.     Allowance  for  the  lattter  is  preferably 
made  by  a  proportionate  increase  in  either  the  live  load  or  the  live  load  stresses.     The 
working  stresses  hereinafter  recommended  are  intended  to  apply  to  the  equivalent  static 
stresses  thus  determined. 

In  the  case  of  high  buildings  the  live  load  on  columns  may  be  reduced  in  accordance  with 
the  usual  practice. 

(6)  Lengths  of  Beams  and  Columns. — The  span  length  for  beams  and  slabs  simply 
supported  should  be  taken  as  the  distance  from  center  to  center  of  supports,  but  need 
not  be  taken  to  exceed  the  clear  span  plus  the  depth  of  beam  or  slab.  For  continuous 
or  restrained  beams  built  monolithically  into  supports  the  span  length  may  be  taken 
as  the  clear  distance  between  faces  of  supports.  Brackets  should  not  be  considered  as 
reducing  the  clear  span  in  the  sense  here  intended,  except  that  when  brackets  which  make 
an  angle  of  45  degrees  or  more  with  the  axis  of  a  restrained  beam  are  built  monolithically 
with  the  beam,  the  span  may  be  measured  from  the  section  where  the  combined  depth 
of  beam  and  bracket  is  at  least  one-third  more  than  the  depth  of  the  beam."  Maximum 
negative  moments  are  to  be  considered  as  existing  at  the  end  of  the  span  as  here  defined. 

When  the  depth  of  a  restrained  beam  is  greater  at  its  ends  than  at  midspan  and  the 
slope  of  the  bottom  of  the  beam  at  its  ends  makes  an  angle  of  not  more  than  15  degress 
with  the  direction  of  the  axis  of  the  beam  at  midspan,  the  span  length  may  be  measured 
from  face  to  face  of  supports. 

The  length  of  columns  should  be  taken  as  the  maximum  unstayed  length. 

(c)  Stresses. — The  following  assumptions  are  recommended  as  a  basis  for  calculations: 

1. — Calculations  will  be  made  with  reference  to  working  stresses  and  safe  loads  rather 
than  with  reference  to  ultimate  strength  and  ultimate  loads. 

2. — A  plane  section  before  bending  remains  plane  after  bending. 

*  From  Final  Report  of  the  Special  Committee  on  Concrete  and  Reinforced  Concrete  of  the  Ameri- 
can Society  of  Civil  Engineers,  presented  before  the  Society,  Jan.  17,  1917. 

243 


3. — The  modulus  of  elasticity  of  concrete  in  compression  is  constant  within  the  usual 
limits  of  working  stresses.  The  distribution  of  comprefisive  stress  in«beams  is,  therefore, 
rectilinear. 

4. — In  calculating  the  moment  of  resistance  of  beams  the  tensile  stresses  in  the  concrete 
are  neglected. 

5. — The  adhesion  between  the  concrete  and  the  reinforcement  is  perfect.  Under 
compressive  stress  the  two  materials  are,  therefore,  stressed  in  proportion  to  their  moduli  of 
elasticity. 

6. — The  ratio  of  the  modulus  of  elasticity  of  steel  to  the  modulus  of  elasticity  of  concrete 
is  taken  at  15,  except  as  modified  in  section  on  "Working  Stresses." 

7. — Initial  stress  in  the  reinforcement  due  to  contraction  or  expansion  of  the  concrete 
is  neglected. 

It  is  recognized  that  some  of  the  assumptions  given  herein  are  not  entirely  borne  out 
by  experimental  data.  They  are  given  in  the  interest  of  simplicity  and  uniformity,  and 
variations  from  exact  conditions  are  taken  into  account  in  the  selection  of  formulas  and 
working  stresses. 

The  deflection  of  a  beam  depends  upon  the  strength  and  stiffness  developed  throughout 
its  length.  For  calculating  deflection  a  value  of  8  for  the  ratio  of  the  moduli  will  give 
results  corresponding  approximately  with  the  actual  conditions. 

T-Beams. — In  beam  and  slab  construction  an  effective  bond  should  be  provided  at 
the  junction  of  the  beam  and  slab.  When  the  principal  slab  reinforcement  is  parallel 
to  the  beam,  transverse  reinforcement  should  be  used  extending  over  the  beam  and  well 
into  the  slab. 

The  slab  may  be  considered  an  integral  part  of  the  beam,  when  adequate  bond  and 
shearing  resistance  between  slab  and  web  of  beam  is  provided,  but  its  effective  width 
shall  be  determined  by  the  following  rules: 

(a) — It  shall  not  exceed  one-fourth  of  the  span  length  of  the  beam. 

(6) — Its  overhanging  width  on  either  side  of  the  web  shall  not  exceed  six  times  the 
thickness  of  the  slab. 

In  the  design  of  continuous  T-beams,  due  consideration  should  be  given  to  the  com- 
pressive stress  at  the  support. 

Beams  in  which  the  T-form  is  used  only  for  the  purpose  of  providing  additional  com- 
pression area  of  concrete  should  preferably  have  a  width  of  flange  not  more  than  three 
times  the  width  of  the  stem  and  a  thickness  of  flange  not  less  than  one-third  of  the  depth 
of  the  beam.  Both  in  this  form  and  in  the  beam  and  slab  form  the  web  stresses  and  the 
limitations  in  placing  and  spacing  the  longitudinal  reinforcement  will  probably  be  control- 
ling factors  in  design. 

Floor  Slabs  Supported  Along  Four  Sides. — Floor  slabs  having  the  supports  extending 
along  the  four  sides  should  be  designed  and  reinforced  as  continuous  over  the  supports. 
If -the  length  of  the  slab  exceeds  1.5  times  its  width  the  entire  load  should  be  carried  by 
transverse  reinforcement. 

For  uniformly  distributed  loads  on  square  slabs,  one-half  the  live  and  dead  load  may 
be  used  in  the  calculations  of  moment  to  be  resisted  in  each  direction.  For  oblong  slabs, 
the  length  of  which  is  not  greater  than  one  and  one-half  times  their  width,  the  moment  to 
be  resisted  by  the  transverse  reinforcement  may  be  found  by  using  a  proportion  of  the  live 

and  dead  load  equal  to  that  given  by  the  formula  r  =  r  —  0.5,  where  I  =  length  and  b  = 

breadth  of  slab.  TJie  longitudinal  reinforcement  should  then  be  proportioned  to  carry 
the  remainder  of  the  load. 

In  placing  reinforcement  in  such  slabs  account  may  well  be  taken  of  the  fact  that 
the  bending  moment  is  greater  near  the  center  of  the  slab  than  near  the  edges.  For  this 
purpose  two-thirds  of  the  previously  calculated  moments  may  be  assumed  as  carried  by  the 
center  half  of  the  slab  and  one-third  by  the  outside  quarters. 

Loads  carried  to  beams  by  slabs  which  are  reinforced  in  two  directions  will  not  be 
uniformly  distributed  to  the  supporting  beams  and  the  distribution  will  depend  on  the 
relative  stiffness  of  the  slab  and  the  supporting  beams.  The  distribution  which  may  be 
expected  ordinarily  is  a  variation  of  the  load  in  the  beam  in  accordance  with  the  ordinates 
of  a  parabola,  having  its  vertex  at  the  middle  of  the  span.  For  any  gn  en  design,  the  prob- 
able distribution  shlould  be  ascertained  and  the  moments  in  the  beam  calculated  accordingly. 

Continuous  Beams  and  Slabs. — When  the  beam  or  slab  is  continuous  over  its  supports, 
reinforcement  should  be  fully  provided  at  points  of  negative  moment;  and  the  stresses  in 
concrete  recommended  in  the  section  on  "Working  Stresses"  should  not  be  exceeded.  In 
computing  the  positive  and  negative  moments  in  beams  and  slabs?  continuous  over  several 
supports,  due  to  uniformly  distributed  loads,  the  following  rules  are  recommended: 

(a)   For  floor  slabs  the  bending  moments  at  center  and  at  support  should  be  taken 

at  jo"  f°r  both  dead  and  live  loads,  where  w  represents  the  load  per  linear  unit  and  I  the 
span  length. 

244 


(6)  For  beams  the  bending  moment  at  center  and  at  support  for  interior  spans  should 

icl~  wl~ 

be  taken  at  y^"'  anc^  f°r  end  spans  it  should  be  taken  at  -r/r  for  center  and  interior  support, 

for  both  dead  and  live  loads. 

(c)  In  the  case  of  beams  and  slabs  continuous  for  two  spans  only,  with  their  ends  re- 
strained, the  bending  moment  both  at  the  central  support  and  near  the  middle  of  the  span 

««/2 

should  be  taken  at  r-Tr* 

(d)  At  the  ends  of  continuous  beams  the  amount  of  negative  moment  which  will  be 
developed  in  the  beam  will  depend  on  the  condition  of  restraint  or  fixedness,  and  this 

will  depend  on  the  form  of  construction  used.     In  the  ordinary  cases  a  moment  of——  may 

10 

be  taken;  for  small  beams  running  into  heavy  columns  this  should  be  increased,  but  not  to 

.wP 

exceed-- 

For  spans  of  unusual  length,  or  for  spans  of  materially  unequal  length,  more  exact 
calculations  should  be  made.  Special  consideration  is  also  required  in  the  case  of  con- 
centrated loads. 

Even  if  the  center  of  the  span  is  designed  for  a  greater  bending  moment  than  is  called 
for  by  (a)  or  (6),  the  negative  moment  at  the  support  should  not  be  taken  as  less  than  the 
values  there  given. 

Where  beams  are  reinforced  on  the  compression  side,  the  steel  may  be  assumed  to 
carry  its  proportion  of  stress  in  accordance  with  the  ratio  of  moduli  of  elasticity,  as  given 
in  the  section  on  "Working  Stresses."  Reinforcing  bars  for  compression  in  beams  should 
be  straight  and  should  be  two  diameters  in  the  clear  from  the  surface  of  the  concrete. 
For  the  positive  bending  moment,  such  reinforcement  should  not  exceed  one  per  cent  of 
the  area  of  the  concrete.  In  the  case  of  cantile"\er  and  continuous  beams,  tensile  and 
compressive  reinforcement  over  supports  should  extend  sufficiently  beyond  the  support 
and  beyond  the  point  of  inflection  to  develop  the  requisite  bond  strength. 

In  construction  made  continuous  over  supports  it  is  important  that  ample  foundations 
should  be  provided;  for  unequal  settlements  are  liable  to  produce  unsightly,  if  not  danger- 
ous cracks.  This  effect  is  more  likely  to  occur  in  low  structures. 

Girders,  such  as  wall  girders,  which  have  beams  framed  into  one  side  only,  should 
be  designed  to  resist  torsional  moment  arising  from  the  negative  moment  at  the  end  of  the 
beam. 

Bond  Strength  and  Spacing  of  Reinforcement. — Adequate  bond  strength  should 
be  provided.  The  formula  hereinafter  given  for  bond  stresses  in  beams  is  for  straight 
longitudinal  bars.  In  beams  in  which  a  portion  of  the  reinforcement  is  bent  up  near  the 
end,  the  bond  stress  at  places,  in  both  the  straight  bars  and  the  bent  bars,  will  be  consider- 
ably greater  than  for  all  the  bars  straight,  and  the  stress  at  some  point  may  be  several  times 
as  much  as  that  found  by  considering  the  stress  to  be  uniformly  distributed  along  the  bar. 
In  restrained  and  cantilever  beams  full  tensile  stress  exists  in  the  reinforcing  bars  at  the 
point  of  support  and  the  bars  should  be  anchored  in  the  support  sufficiently  to  develop 
this  stress. 

In  case  of  anchorage  of  bars,  an  additional  length  of  bar  should  be  provided  beyond 
that  found  on  the  assumption  of  uniform  bond  stress,  for  the  reason  that  before  the  bond 
resistance  at  the  end  of  the  bar  can  be  developed  the  bar  may  have  begun  to  slip  at  another 
point  and  "running"  resistance  is  less  than  the  resistance  before  slip  begins. 

Where  high  bond  resistance  is  required,  the  deformed  bar  is  a  suitable  means  of  supply- 
ing the  necessary  strength.  But  it  should  be  recognized  that  even  with  a  deformed  bar 
initial  slip  occurs  at  early  loads,  and  that  the  ultimate  loads  obtained  in  the  usual  tests 
for  bond  resistance  may  be  misleading.  Adequate  bond  strength  throughout  the  length 
of  a  bar  is  preferable  to  end  anchorage,  but,  as  an  additional  safeguard,  such  anchorage  may 
properly  be  used  in  special  cases.  Anchorage  furnished  by  short  bends  at  a  right  angle  is 
less  effective  than  by  hooks  consisting  of  turns  through  180  degrees. 

The  lateral  spacing  of  parallel  bars  should  be  not  less  than  three  diameters  from  center 
to  center,  nor  should  the  distance  from  the  side  of  the  beam  to  the  center  of  the  nearest 
bar  be  less  than  two  diameters.  The  clear  spacing  between  two  layers  of  bars  should  be  not 
less  than  one  inch.  The  use  of  more  than  two  layers  is  not  recommended,  unless  the  layers 
are  tied  together  by  adequate  metal  connections,  particularly  at  and  near  points  where 
bars  are  bent  up  or  bent  down.  Where  more  than  one  layer  is  used,  at  least  all  bars  above 
the  lower  layer  should  be  bent  up  and  anchored  beyond  the  edge  of  the  support. 

Diagonal  Tension  and  Shear. — When  a  reinforced  concrete  beam  is  subjected  to  flexural 
action,  diagonal  tensile  stresses  are  set  up.  A  beam  without  web  reinforcement  will  fail 
if  these  stresses  exceed  the  tensile  strength  of  the  concrete.  When  web  reinforcement, 
made  up  of  stirrups  or  of  diagonal  bars  secured  to  the  longitudinal  reinforcement,  or  of 
longitudinal  reinforcing  bars  bent  up  at  several  points,  is  used,  new  conditions  prevail,  but 

245 


even  in  this  case  at  the  beginning  of  loading  the  diagonal  tension  developed  is  taken  princi- 
pally by  the  concrete,  the  deformations  which  are  developed  in  the  concrete  permitting 
but  little  stress  to  be  taken  by  the  web  reinforcement.  When  the  resistance  of  the  concrete 
to  the  diagonal  tension  is  overcome  at  any  point  in  the  depth  of  the  beam,  greater  stress  is 
at  once  set  up  in  the  web  reinforcement. 

For  homogeneous  beams  the  analytical  treatment  of  diagonal  tension  is  not  very 
complex,  the  diagonal  tensile  stress  is  a  function  of  the  horizontal  and  vertical  shear- 
ing stresses  and  of  the  horizontal  tensile  stress  at  the  point  considered,  an  as  the  intensity 
of  these  three  stresses  varies  from  the  neutral  axis  to  the  remotest  fibre,  the  intensity 
of  the  diagonal  tension  will  be  different  at  different  points  in  the  section,  and  will  change 
with  different  proportionate  dimensions  of  length  to  depth  of  beam.  For  the  composite 
structure  of  reinforced  concrete  beams,  an  analysis  of  the  web  stresses,  and  particularly 
of  the  diagonal  tensile  stresses,  is  very  complex;  and  when  the  variations  due  to  a  change 
from  no  horizontal  tensile  stress  in  the  concrete  at  remotest  fibre  to  the  presence  of  hori- 
zontal tensile  stress  at  some  point  below  the  neutral  axis  are  considered,  the  problem 
becomes  more  complex  and  indefinite.  Under  these  circumstances,  in  designing  recourse 
is  had  to  the  use  of  the  calculated  vertical  shearing  stress  as  a  means  of  comparing  or 
measuring  the  diagonal  tensile  stresses  developed,  it  being  understood  that  the  vertical 
shearing  stress  is  not  the  numerical  equivalent  of  the  diagonal  tensile  stress,  and  that  there 
is  not  even  a  constant  ratio  between  them.  It  is  here  recommended  that  the  maximum 
vertical  shearing  stress  in  a  section  be  used  as  the  means  of  comparison  of  the  resistance  to 
diagonal  tensile  stress  developed  in  the  concrete  in  beams  not  having  web  reinforcement. 

Even  after  the  concrete  has  reached  its  limit  of  resistance  to  diagonal  tension,  if  the 
beam  has  web  reinforcement,  conditions  of  beam  action  will  continue  to  prevail,  at  least 
through  the  compression  area,  and  the  web  reinforcement  will  be  called  on  to  resist  only  a 
part  of  the  web  stresses.  From  experiments  with  beams  it  is  concluded  that  it  is  safe 
practice  to  use  only  two-thirds  of  the  external  vertical  shear  in  making  calculations  of  the 
stresses  that  come  on  stirrups,  diagonal  web  pieces,  and  bent-up  bars,  and  it  is  here 
recommended  for  calculations  in  designing  that  two-thirds  of  the  external  vertical  shear 
be  taken  as  producing  stresses  in  web  reinforcement. 

It  is  well  established  that  vertical  members  attached  to  or  looped  about  horizontal 
members,  inclined  members  secured  to  horizontal  members  in  such  a  way  as  to  insure 
against  slip,  and  the  bending  of  a  part  of  the  longitudinal  reinforcement  at  an  angle, 
will  increase  the  strength  of  a  beam  against  failure  by  diagonal  tension,  and  that  a  well- 
designed  and  well-distributed  web  reinforcement  may  under  the  best  conditions  increase 
the  total  vertical  shear  carried  to  a  value  as  much  as  three  times  that  obtained  when  the 
bars  are  all  horizontal  and  no  web  reinforcement  is  used. 

When  web  reinforcement  comes  into  action  as  the  principal  tension  web  resistance, 
the  bond  stresses  between  the  longitudinal  bars  and  the  concrete  are  not  distributed 
as  uniformly  along  the  bars  as  they  otherwise  would  be,  but  tend  to  be  concentrated 
at  and  near  stirrups,  and  at  and  near  the  points  where  bars  are  bent  up.  When  stirrups 
are  not  rigidly  attached  to  the  longitudinal  bars,  and  the  proportioning  of  bars  and  stirrups 
spacing  is  such  that  local  slip  of  bars  occurs  at  stirrups,  the  effectiveness  of  the  stirrups 
is  impaired,  though  the  presence  of  stirrups  still  gives  an  element  of  toughness  against 
diagonal  tension  failure. 

Sufficient  bond  resistance 'between  the  concrete  and  the  stirrups  or  diagonals  must 
be  provided  in  the  compressing  area  of  the  beam/ 

The  longitudinal  spacing  of  vertical  stirrups  should  not  exceed  one-half  the  depth  of 
beam,  and  that  of  inclined  members  should  not  exceed  three-fourths  of  the  depth  ef  beam. 

Bending  of  longitudinal  reinforcing  bars  at  an  angle  across  the  web  of  the  beam  may 
be  considered  as  adding  to  diagonal  tension  resistance  for  a  horizontal  distance  from  the 
point  of  bending  equal  to  three-fourths  of  the  depth  of  beam.  Where  the  bending  is  made 
at  two  or  more  points,  the  distance  between  points  of  bending  should  not  exceed  three- 
fourths  of  the  depth  of  the  beam.  In  the  case  of  a  restrained  beam  the  effect  of  bending  up 
a  bar  at  the  bottom  of  the  beam  in  resisting  diagonal  tension  may  not  be  taken  as  extending 
beyond  a  section  at  the  point  of  inflection,  and  the  effect  of  bending  down  a  bar  in  the 
region  of  negative  moment  may  be  taken  as  extending  from  the  point  of  bending  down  of 
bar  nearest  the  support  to  a  section  not  more  than  three-fourths  of  the  depth  of  beam  beyond 
the  point  of  bending  down  of  bar  farthest  from  the  support  but  not  beyond  the  point  of 
inflection.  In  case  stirrups  are  used  in  the  beam  away  from  the  region  in  which  the  bent 
bars  are  considered  effective,  a  stirrup  should  be  placed  not  farther  than  a  distance  equal 
to  one-fourth  the  depth  of  beam  from  the  limiting  sections  defined  above.  In  case  the 
web  resistance  required  through  the  region  of  bent  bars  is  greater  than  that  furnished  by 
the  bent  bars,  sufficient  additional  web  reinforcement  in  the  form  of  stirrups  or  attached 
diagonals  should  be  provided.  The  higher  resistance  to  diagonal  tension  stresses  given  by 
unit  frames  having  the  stirrups  and  bent-up  bars  securely  connected  together  both  longi- 
tudinally and  laterally  is  worthy  of  recognition.  It  is  necessary  that  a  limit  be  placed 

246 


on  the  amount  of  shear  which  may  be  allowed  in  a  beam;  for  when  web  reinforcement 
sufficiently  efficient  to  give  very  high  web  resistance  is  used,  at  the  higher  stresses  the 
concrete  in  the  beam  becomes  checked  and  cracked  in  such  a  way  as  to  endanger  its  dura- 
bility as  well  as  its  strength. 

The  section  to  be  taken  as  the  critical  section  in  the  calculation  of  shearing  stresses 
will  generally  be  the  one  having  the  maximum  vertical  shear,  though  experiments  show 
that  the  section  at  which  diagonal  tension  failures  occur  is  not  just  at  a  support  even  though 
the  shear  at  the  latter  point  be  much  greater. 

In  the  case  of  restrained  beams,  the  first  stirrup  or  the  point  of  bending  down  of  bar 
should  be  placed  not  farther  than  one-half  of  the  depth  of  beam  away  from  the  face  of  the 
support. 

It  is  important  that  adequate  bond  strength  or  anchorage  be  provided  to  develop 
fully  the  assumed  strength  of  all  web  reinforcement. 

Low  bond  stresses  in  the  longitudinal  bars  are  helpful  in  giving  resistance  against 
diagonal  tension  failures  and  anchorage  of  longitudinal  bars  at  the  ends  of  the  beams 
or  in  the  supports  is  advantageous. 

It  should  be  noted  that  it  is  on  the  tension  side  of  a  beam  that  diagonal  tension  develops 
in  a  critical  way,  and  that  proper  connection  should  always  be  made  between  stirrups  or 
other  web  reinforcement  and  the  longitudinal  tension  reinforcement,  whether  the  latter  is 
on  the  lower  side  of  the  beam  or  on  its  upper  side.  Where  negative  moment  exists,  as  is 
the  case  near  the  supports  in  a  continuous  beam,  web  reinforcement  to  be  effective  must  be 
looped  over  or  wrapped  around  or  be  connected  with  the  longitudinal  tension  reinforcing 
bars  at  the  top  of  the  beam  in  the  same  way  as  is  necessary  at  the  bottom  of  the  beam  at 
sections  where  the  bending  moment  is  positive. 

Inasmuch  as  the  smaller  the  longitudinal  deformations  in  the  horizontal  reinforce- 
ment are,  the  less  the  tendency  for  the  formation  of  diagonal  cracks,  a  beam  will  be  strength- 
ened against  diagonal  tension  failure  by  so  arranging  and  proportioning  the  horizontal 
reinforcement  that  the  unit  stresses  at  points  of  large  shear  shall  be  relatively  low. 

It  does  not  seem  feasible  to  make  a  complete  analysis  of  the  action  of  web  reinforce- 
ment, and  more  or  less  empirical  methods  of  calculation  are  therefore  employed.  Limiting 
values  of  working  stresses  for  different  types  of  web  reinforcement  are  given  in  the  section 
on  "Working  Stresses."  The  conditions  apply  to  cases  commonly  met  in  design.  It  is 
assumed  that  adequate  bond  resistance  or  anchorage  of  all  web  reinforcement  will  be 
provided. 

When  a  flat  slab  rests  on  a  column,  or  a  column  bears  on  a  footing,  the  vertical  shearing 
stresses  in  the  slab  or  footing  immediately  adjacent  to  the  column  are  termed  punching 
shearing  stresses.  The  element  of  diagonal  tension,  being  a  function  of  the  bending 
moment  as  well  as  of  shear,  may  be  small  in  such  cases,  or  may  be  otherwise  provided  for. 
For  this  reason  the  permissible  limit  of  stress  for  punching  shear  may  be  higher  than  the 
allowable  limit  when  the  shearing  stress  is  used  as  a  means  of  comparing  diagonal  tensile 
stress.  The  working  values  recommended  are  given  in  the  section  on  "Working  Stresses." 

Columns. — By  columns  are  meant  compression  members  of  which  the  ratio  of  unsup- 
ported length  to  least  width  exceeds  about  four,  and  which  are  provided  with  reinforcement 
of  one  of  the  forms  hereafter  described. 

It  is  recommended  that  the  ratio  of  unsupported  length  of  column  to  its  least  width  be 
limited  to  fifteen. 

The  effective  area  of  hooped  columns  or  columns  reinforced  with  structural  shapes 
shall  be  taken  as  the  area  within  the  circle  enclosing  the  spiral  or  the  polygon  enclosing  the 
structural  shapes. 

Columns  may  be  reinforced  by  longitudinal  bars;  by  bands,  hoops,  or  spirals,  together 
with  longitudinal  bars;  or  by  structural  forms  which  are  sufficiently  rigid  to  have  value  in 
themselves  as  columns.  The  general  effect  of  closely  spaced  hooping  is  to  greatly  increase 
the  toughness  of  the  column  and  to  add  to  its  ultimate  strength,  but  hooping  has  little 
effect  on  its  behavior  within  the  limit  of  elasticity.  It  thus  renders  the  concrete  a  safer  and 
more  reliable  material,  and  should  permit  the  use  of  a  somewhat  higher  working  stress. 
The  beneficial  effects  of  toughening  are  adequately  provided  by  a  moderate  amount  of 
hooping,  a  larger  amount  serving  mainly  to  increase  the  ultimate  strength  and  the  deforma- 
tion possible  before  ultimate  failure. 

Composite,  columns  of  structural  steel  and  concrete  in  which  the  steel  forms  a  column 
by  itself  should  be  designed  with  caution.  To  classify  this  type  as  a  concrete  column 
reinforced  with  structural  steel  is  hardly  permissible,  as  the  steel,  generally,  will  take 
the  greater  part  of  the  load.  When  this  type  of  column  is  used,  the  concrete  should 
be  adequately  tied  together  by  tie  plates  or  lattice  bars,  which,  together  with  other  details, 
such  as  splices,  etc.,  should  be  designed  in  conformity  with  standard  practice  for  structural 
steel.  The  concrete  may  exert  a  beneficial  effect  in  restraining  the  steel  from  lateral 
deflection  and  also  in  increasing  the  carrying  capacity  of  the  column.  The  proportion  of 
load  to  be  carried  by  the  concrete  will  depend  on  the  form  of  the  column  and  the  method  of 

247 


construction.  Generally,  for  high  percentages  of  steel,  the  concrete  will  develop  relatively 
low  unit  stresses,  and  caution  should  be  used  in  placing  dependence  on  the  concrete. 

The  following  recommendations  are  made  for  the  relative  working  stresses  in  the 
concrete  for  the  several  types  of  columns: 

(a)  Columns  with  longitudinal  reinforcement  to  the  extent  of  not  less  than  1  per  cent 
and  not  more  than  4  per  cent,  and  with  lateral  ties  of  not  less  than  34  inch  in  diameter 
12  inches  apart,  nor  more  than  16  diameters  of  the  longitudinal  bar:  the  unit  stress  rec- 
ommended for  axial  compression,  on  concrete  piers  having  a  length  not  more  than  four 
diameters,  in  section  on  "Working  Stresses." 

(6)  Columns  reinforced  with  not  less  than  1  per  cent  and  not  more  than  4  per  cent 
of  longitudinal  bars  and  with  circular  hoops  or  spirals  not  less  than  1  per  cent  of  the  volume 
of  the  concrete  and  as  hereinafter  specified :  a  unit  stress  55  per  cent  higher  than  given  for 
(a),  provided  the  ratio  of  unsupported  length  of  column  to  diameter  of  the  hooped  core  is 
not  more  than  10. 

The  foregoing  recommendations  are  based  on  the  following  conditions: 

It  is  recommended  that  the  minimum  size  of  columns  to  which  the  working  stresses 
may  be  applied  be  12  inches  out  to  out. 

In  all  cases  longitudinal  reinforcement  is  assumed  to  carry  its  proportion  of  stress  in 
accordance  with  (c)  Stresses,  page  243.  The  hoops  or  bands  are  not  to  be  counted  on 
directly  as  adding  to  the  strength  of  the  column. 

Longitudinal  reinforcement  bars  should  be  maintained  straight,  and  should  have  suffi- 
cient lateral  support  to  be  securely  held  in  place  until  the  concrete  has  set. 

Where  hooping  is  used,  the  total  amount  of  such  reinforcement  shall  be  not  less  than 
1  per  cent  of  the  volume  of  the  column,  enclosed.  The  clear  spacing  of  such  hooping 
shall  not  be  greater  than  one-sixth  the  diameter  of  the  enclosed  column  and  preferably 
not  greater  than  one- tenth,  and  in  no  case  more  than  2%  in.  Hooping  is  to  be  circular 
and  the  ends  of  bands  must  be  united  in  such  a  way  as  to  develop  their  full  strength. 
Adequate  means  must  be  provided  to  hold  bands  or  hoops  in  place  so  as  to  form  a  column, 
the  core  of  which  shall  be  straight  and  well  centered.  The  strength  of  hooped  columns 
depends  very  much  upon  the  ratio  of  length  to  diameter  of  hooped  core,  and  the  strength 
due  to  hooping  decreases  rapidly  as  this  ratio  increases  beyond  five.  The  working  stresses 
recommended  are  for  hooped  columns  with  a  length  of  not  more  than  ten  diameters  of  the 
hooped  core. 

The  Committee  has  no  recommendation  to  make  for  a  formula  for  working  stresses 
for  columns  longer  than  ten  diameters. 

Bending  stresses  due  to  eccentric  loads,  such  as  unequal  spans  of  beams,  and  to  lateral 
forces,  must  be  provided  for  by  increasing  the  section  until  the  maximum  stress  does 
not  exceed  the  values  above  specified.  Where  tension  is  possible  in  the  longitudinal 
bars  of  the  columns,  adequate  connection  between  the  ends  of  the  bars  must  be  provided 
to  take  this  tension. 

Reinforcing  for  Shrinkage  and  Temperature  Stresses. — When  areas  of  concrete  too 
large  to  expand  and  contract  freely  as  a  whole  are  exposed  to  atmospheric  conditions, 
the  changes  of  form  due  to  shrinkage  and  to  action  of  temperature  are  such  that  cr  cks  may 
occur  in  the  mass  unless  precautions  are  taken  to  distribute  the  stresses  so  as  to  prevent  the 
cracks  altogether  or  to  render  them  very  small.  The  distance  apart  of  the  cracks,  and 
consequently  their  size,  will  be  directly  proportional  to  the  diameter  of  the  reinforcement 
and  to  the  tensile  strength  of  the  concrete,  and  inversely  proportional  to  the  percentage  of 
reinforcement  and  also  to  its  bond  resistance  per  unit  of  surface  area.  To  be  most  effective, 
therefore,  reinforcement  (in  amount  generally  not  less  than  one-third  of  1  per  cent  of  the 
gross  area)  of  a  form  which  \vill  develop  a  high  bond  resistance  should  be  placed  near  the 
exposed  surface  and  be  well  distributed.  Where  openings  occur  the  area  of  cross-section  of 
the  reinforcement  should  not  be  reduced.  The  allowable  size  and  spacing  of  cracks  depends 
on  various  considerations,  such  as  the  necessity  for  water-tightness,  the  importance  of 
appearance  of  the  surface,  and  the  atmospheric  changes. 

The  tendency  of  concrete  to  shrink  makes  it  necessary,  except  where  expansion  is 
-  provided  for,  to  thoroughly  connect  the  component  parts  of  the  frame  of  articulated 
structures,  such  as  floor  and  wall  members  in  buildings,  by  the  use  of  suitable  reinforcing 
material.  The  amount  of  reinforcement  for  such  connection  should  bear  some  relation  to 
the  size  of  the  members  connected,  larger  and  heavier  members  requiring  stronger  connec- 
tions. The  reinforcing  bars  should  be  extended  beyond  the  critical  section  far  enough,  or 
should  be  sufficiently  anchored  to  develop  their  full  tensile  strength. 

Flat  Slab. — The  continuous  flat  slab  reinforced  in  two  or  more  directions  and  built 
monolithically  with  the  supporting  columns  (without  beams  or  girders)  is  a  type  of  construc- 
tion which  is  now  extensively  used  and  which  has  recognized  advantages  for  certain 
types  of  structures  as,  for  example,  warehouses  in  which  large,  open  floor  space  is  desired. 
In  its  construction,  there  is  excellent  opportunity  for  inspecting  the  position  of  the  re- 
inforcement, The  conditions  attending  deposition  and  placing  of  concrete  are  favorable  to 

24S 


securing  uniformity  and  soundness  in  the  concrete.     The  recommendations  in  the  following 
paragraphs  relate  to  flat  slabs  extending  over  several  rows  of  panels  in 'each  direction. 
Necessarily  the  treatment  is  more  or  less  empirical. 

The  co-efficients  and  moments  given  relate  to  uniformly  distributed  loads. 

(a)  Column  Capital. — It  is  usual  in  flat  slab  construction  to  enlarge  the  supporting 
columns  at  their  top,  thus  forming  column  capitals.  The  size  and  shape  of  the  column 
capital  affect  the  strength  of  the  structure  in  several  ways.  The  moment  of  the  external 
forces  which  the  slab  is  called  upon  to  resist  is  dependent  upon  the  size  of  the  capital; 
the  section  of  the  slab  immediately  above  the  upper  periphery  of  the  capital  carries  the 
highest  amount  of  punching  shear;  and  the  bending  moment  developed  in  the  column 
by  an  eccentric  or  unbalanced  loading  of  the  slab  is  greatest  at  the  under  surface  of  the 
slab.  Generally  the  horizontal  section  of  the  column  capital  should  be  round  or  square 
with  rounded  corners.  In  oblong  panels  the  section  may  be  oval  or  oblong,  with  dimensions 
proportional  to  the  panel  dimensions.  For  computation  purposes,  the  diameter  of  the 
column  capital  will  be  considered  to  be  measured  where  its  vertical  thickness  is  at  least 
lj^  inches,  provided  the  slope  of  the  capital  below  this  point  nowhere  makes  an  angle  with 
the  vertical  of  more  than  45  degrees.  In  case  a  cap  is  placed  above  the  column  capital, 
the  part  of  this  cap  within  a  cone  made  by  extending  the  lines  of  the  column  capital  upward 
at  the  slope  of  45  degrees  to  the  bottom  of  the  slab  or  dropped  panel  may  be  considered  as 
part  of  the  column  capital  in  determining  the  diameter  for  design  purposes.  Without 
attempting  to  limit  the  size  of  the  column  capital  for  special  cases,  it  is  recommended  that 
the  diameter  of  the  column  capital  (or  its  dimensions  parallel  to  the  edge  of  the  panel) 
generally  be  made  not  less  than  one-fifth  of  the  dimension  of  the  panel  from  center  to 
center  of  adjacent  columns.  A  diameter  equal  to  0.225  of  the  panel  length  has  been  used 
quite  widely  and  acceptably.  For  heavy  loads  or  large  panels  especial  attention  should  be 
given  to  designing  and  reinforcing  the  column  capital  with  respect  to  compressive  stresses 
and  bending  moments.  In  the  case  of  heavy  loads  or  large  panels,  and  where  the  conditions 
of  the  panel  loading  or  variations  in  panel  length  or  other  conditions  cause  high  bending 
stresses  in  the  column,  and  also  for  column  capitals  smaller  than  the  size  herein  recom- 
mended, especial  attention  should  be  given  to  designing  and  reinforcing  the  column  capital 
with  respect  to  compression  and  to  rigidity  of  connection  to  floor  slab. 

(6)  Dropped  Panel. — In  one  type  of  construction  the  slab  is  thickened  throughout 
an  area  surrounding  the  column  capital.  The  square  or  oblong  of  thickened  slab  thus 
formed  is  called  a  dropped  panel  or  a  drop.  The  thickness  and  the  width  of  the  dropped 
panel  may  be  governed  by  the  amount  of  resisting  moment  to  be  provided  (the  com- 
pressive stress  in  the  concrete  being  dependent  upon  both  thickness  and  width),  or  its 
thickness  may  be  governed  by  the  resistance  to  shear  required  at  the  edge  of  the  column 
capital  and  its  width  by  the  allowable  compressive  stresses  and  shearing  stresses  in  the 
thinner  portion  of  the  slab  adjacent  to  the  dropped  panel.  Generally,  however,  it  is 
recommended  that  the  width  of  the  dropped  panel  be  at  least  four-tenths  of  the  correspond- 
ing side  of  the  panel  as  measureU  from  center  to  center  of  columns,  and  that  the  offset  in 
thickness  be  not  more  than  five- tenths  of  the  thickness  of  the  slab  outside  the  dropped 
panel. 

(c)  Slab  Thickness. — In  the  design  of  a  slab,  the  resistance  to  bending  and  to  shear- 
ing forces  will  largely  govern  the  thickness,  and,  in  the  case  of  large  panels  with   light 
loads,  resistance  to  deflection  may  be  a  controlling  factor.     The  following  formulas  for 
minimum  thicknesses  are  recommended  as  general  rules  of  design  when  the  diameter 
of  the  column  capital  is  not  less  than  one^fifth  of  the  dimension  of  the  panel  from  center  to 
center  of  adjacent  columns,  the  large  dimension  being  used  in  the  case  of  oblong  panels. 
For  notation,  let 

t  =  total  thickness  of  slab  in  inches. 
L  =  panel  length  in  feet. 
w  =  sum  of  live  load  and  dead  load  in  pounds  per  square  foot. 

Then,  for  a  slab  without  dropped  panels,  minimum  t  =  0.024L\/w  -f  1^;  for  a  slab 
with  dropped  panels,  minimum  I  =  Q.Q2L'vw  +  1;  for  a  dropped  panel  whose  width  is 
four- tenths  of  the  panel  length,  minimum  t  =  0.03L\A0  +  lM- 

In  no  case  should  the  slab  thickness  be  made  less  than  six  inches,  nor  should  the  thick- 
ness of  a  floor  slab  be  made  less  than  one-thirty-second  of  the  panel  length,  nor  the  thick- 
ness of  a  roof  slab  less  than  one-fortieth  of  the  panel  length. 

(d)  Bending  and  Resisting  Moments  in  Slabs. — If  a  vertical  section  of  a  slab  be  taken 
across    a   panel  along  a  line  midway  between  columns,  and  if  another  section  be  taken 
along  an  edge  of  the  panel  parallel  to  the  first  section,  but  skirting  the  part  of  the  periphery 
of  the  column  capitals  at  the  two  corners  of  the  panels,  the  moment  of  the  couple  formed  by 
the  external  load  on  the  half  panel,  exclusive  of  that  over  the  column  capital  (sum  of  dead 
and  live  load)  and  the  resultant  of  the  external  shear  or  reaction  at  the  support  at  the 

249 


two  column  capitals  (see  Fig.  1),  may  be  found  by  ordinary  static  analysis.  It  will  be  noted 
that  the  edges  of  the  area  here  considered  are  along  lines  of  zero  shear  except  around  the 
column  capitals.  This  moment  of  the  external  forces  acting  on  the  half  panel  will  be 
resisted  by  the  numerical  sum  of  (a)  the  moment  of  the  internal  stresses  at  the  section  of 
the  panel  midway  between  columns  (positive  resisting  moment)  and  (b)  the  moment  of  the 
internal  stresses  at  the  section  referred  to  at  the  end  of  the  panel  (negative  resisting 
moment).  In  the  curved  portion  of  the  end  section  (that  skirting  the  column),  the  stresses 
considered  are  the  components  which  act  parallel  to  the  normal  stresses  on  the  straight 
portion  of  the  section.  Analysis  shows  that,  for  a  uniformly  distributed  load,  and  round 


peripheries  of -fin 
column  caprta/s 

...7° 


section 


section 


FIG.  1. 


FIG.  2. 


columns,  and  square  panels,  the  numerical  sum  of  the  positive  moment  and  the  negative 
moment  at  the  two  sections  named  is  given  quite  closely  by  the  equation 


In  this  formula  and  in  those  which  follow  relating  to  oblong  panels: 
w  =  sum  of  the  live  and  dead  load  per  unit  of  area. 
I  =  side  of  a  square  panel  measured  from  center  to  center  of  columns. 
h  =  one  side  of  the  oblong  panel  measured  from  center  to  center  of  columns. 
fa  =  other  side  of  oblong  panel  measured  in  the  same  way. 
c  =  diameter  of  the  column  capital. 

Mx  =  numerical  sum  of  positive  moment  and  negative  moment  in  one  direction. 
My  =  numerical  sum  of  positive  moment  and  negative  moment  in  the  other  direction. 
(See  paper  and  closure,  Statical  Limitations  upon  the  Steel  Requirement  in  Reinforced 
Concrete  Flat  Slab  Floors,  by  John  R.  Nichols,  Jun.  Am.  Soc.  C.  E.,  Transactions  Am.  Soc. 
C.  E.  Vol.  LXXVII.) 

For  oblong  panels,  the  equations  for  the  numerical  sums  of  the  positive  moment  arid 
the  negative  moment  at  the  two  sections  named  become 


-!  •*(,.-!)' 


Where  Mx  —  is  the  numerical  sum  of  the  positive  moment  and  the  negative  moment 
for  the  sections  parallel  to  the  dimensions  fa,  and  My  is  the  numerical  sum  of  the  positive 
moment  and  the  negative  moment  for  the  sections  parallel  to  the  dimensions  h. 

What  proportion  of  the  total  resistance  exists  as  positive  moment  and  what  as  negative 
moment  is  not  readily  determined.  The  amount  of  the  positive  moment  and  that  of  the 
negative  moment  may  be  expected  to  vary  somewhat  with  the  design  of  the  slab.  It  seems 
proper,  however,  to  make  the  division  of  total  resisting  moment  in  the  ratio  of  three-eighths 
for  the  positive  moment  to  five-eighths  for  the  negative  moment. 

With  reference  to  variations  in  stress  along  the  sections,  it  is  evident  from  condi- 
tions of  flexure  that  the  resisting  moment  is  not  distributed  uniformly  along  either  the 
section  of  positive  moment  or  that  of  negative  moment.  As  the  law  of  the  distribution  is 
not  known  definitely,  it  will  be  necessary  to  make  an  empirical  apportionment  along  the 
sections;  and  it  will  be  considered  sufficiently  accurate  generally  to  divide  the  sections  into 
two  parts  and  to  use  an  average  value  over  each  part  of  the  panel  section. 

The  relatively  large»breadth  of  structure  in  a  flat  slab  makes  the  effect  of  local  variations 
in  the  concrete  less  than  would  be  the  case  for  narrow  members  like  beams.  The  tensile 
resistance  of  the  concrete  is  less  affected  by  cracks.  Measurements  of  deformations  in 

250 


buildings  under  heavy  load  indicate  the  presence  of  considerable  tensile  resistance  in  the 
concrete,  and  the  presence  of  this  tensile  resistance  acts  to  decrease  the  intensity  of  the 
compressive  stresses.  It  is  believed  that  the  use  of  moment  coefficients  somewhat  less 
than  those  given  in  a  preceding  paragraph  as  derived  by  analysis  is  warranted,  the  calcula- 
tions of  resisting  moment  and  stresses  in  concrete  and  reinforcement  being  made  according 
to  the  assumptions  specified  in  this  report  and  no  change  being  made  in  the  values  of  the 
working  stresses  ordinarily  used.  Accordingly,  the  values  of  the  moments  which  are 
recommended  for  use  are  somewhat  less  than  those  derived  by  analysis.  The  values 
given  may  be  used  when  the  column  capitals  are  round,  oval,  square  or  oblong. 

(e)  Names  for  Moment  Sections. — For  convenience,  that  portion  of  the  section  across 
a  panel  along  a  line  midway  between  columns  which  lies  within  the  middle  two  quarters 
of  the  width  of  the  panel  (HI,  Fig.  2),  will  be  called  the  inner  section,  and  that  portion  in 
the  two  outer  quarters  of  the  width  of  the  panel  (GH  and  IJ,  Fig.  2)  will  be  called  the  outer 
sections.  Of  the  section  which  follows  a  panel  edge  from  column  capital  to  column  capital 
and  which  includes  the  quarter  peripheries  of  the  edges  of  two  column  capitals,  that  portion 
within  the  middle  two  quarters  of  the  panel  width  (CD,  Fig.  2)  will  be  called  the  mid- 
section,  and  the  two  remaining  portions  (ABC  and  DEF,  Fig.  2),  each  having  a  projected 
width  equal  to  one-fourth  of  the  panel  width,  will  be  called  the  column-head  sections. 

(/)  Positive  Moment. — For  a  square  interior  panel,  it  is  recommended  that  the  positive 
moment  for  a  section  in  the  middle  of  a  panel  extending  across  its  width  be  taken 

as  —  wl[  I  —  TT  )   .     Of  this  moment,  at  least  25  per  cent  should  be  provided  for  in  the 

25       \         6  / 

inner  section;  in  the  two  outer  sections  of  the  panel  at  least  55  per  cent  of  the  specified 
moment  should  be  provided  for  in  slabs  not  having  dropped  panels,  and  at  least  60  per  cent 
in  slabs  having  dropped  panels,  except  that  in  calculations  to  determine  necessary  thickness 
of  slab  away  from  the  dropped  panel  at  least  70  per  cent  of  the  positive  moment  should  be 
considered  as  acting  in  the  two  outer  sections. 

(Q)  Negative  Moment. — For  a  square  interior  panel,  it  is  recommended  that  the  negative 
moment  for  a  section  \\  hich  follows  a  panel  edge  from  column  capital  to  column  capital  and 
which  includes  the  quarter  peripheries  of  the  edges  of  the  two  column  capitals  (the  section 

1         /        2c\  2 
altogether  forming  the  projected  width  of  the  panel)  be  taken  as  —  u-ll  I-  —  —  \   .     Of  this 

negative  moment,  at  least  20  per  cent  should  be  provided  for  in  the  mid-section  and  at  least 
65  per  cent  in  the  two  column-head  sections  of  the  panel,  except  that  in  slabs  having  dropped 
panels  at  least  80  per  cent  of  the  specified  negative  moment  should  be  provided  for  in  the 
two  column-head  sections  of  the  panel. 

(h)  Moments  for  Oblong  Panels. — When  the  length  of  a  panel  does  not  exceed  the  breadth 
by  more  than  5  per  cent,  computation  may  be  made  on  the  basis  of  a  square  panel  with  sides 
equal  to  the  mean  of  the  length  and  the  breadth. 

When  the  long  side  of  an  interior  oblong  panel  exceeds  the  short  side  by  more  than 
one-twentieth  and  by  not  more  than  one-third  of  the  short  side,  it  is  recommended  that 

the  positive  moment  be  taken  as  —wlz  l/i 5-  J     on  a  section  parallel  to  the  dimension 

h,  and  —  wl\  (h  —  TT  )    on  a  section  parallel  to  dimension  Zi;  and  that  the  negative  moment 
25        V  «/ 

be  taken  as  — -  wh  [h ^ )     on  a  section  at  the  edge  of  the  panel  corresponding  to  the 


2c2 

dimension  h,  and  —  irli  (h ^  1     at  a  section  in  the  other  direction.     The  limitations  of 

the  apportionment  of  moment  between  inner  section  and  outer  section  and  between  mid- 
section  and  column-head  sections  may  be  the  same  as  for  square  panels. 

(t)  Watt  Panels. — The  coefficient  of  negative  moment  at  the  first  row  of  columns 
away  from  the  wall  should  be  increased  20  per  cent  over  that  required  for  interior  panels, 
and  likewise  the  coefficient  of  positive  moment  at  the  section  halfway  to  the  wall  should 
be  increased  by  20  per  cent.  If  girders  are  not  provided  along  the  wall  or  the  slab  does  not 
project  as  a  cantilever  beyond  the  column  line,  the  reinforcement  parallel  to  the  wall  for  the 
negative  moment  in  the  column-head  section  and  for  the  positive  moment  in  the  outer 
section  should  be  increased  by  20  per  cent.  If  the  wall  is  carried  by  the  slab  this  concen- 
trated load  should  be  provided  for  in  the  design  of  the  slab.  The  coefficient  of  negative 
moments  at  the  wall  to  take  bending  in  the  direction  perpendicular  to  the  wall  line  may  be 
determined  by  the  conditions  of  restraint  and  fixedness  as  found  from  the  relative  stiffness 
of  columns  and  slab,  but  in  no  case  should  it  be  taken  as  less  than  one-half  of  that  for 
interior  panels. 

0')  Reinforcement. — In  the  calculation  of  moments  all  the  reinforcing  bars  which  cross 
the  section  under  consideration  and  which  fulfill  the  requirements  given  under  paragraph 
(I)  of  this  chapter  may  be  used.  For  a  column-head  section  reinforcing  bars  parallel  to  the 

251 


straight  portion  of  the  section  do  not  contribute  to  the  negative  resisting  moment  for  the 
column-head  section  in  question.  In  the  case  of  four-way  reinforcement  the  sectional  area 
of  the  diagonal  bars  multiplied  by  the  sine  of  the  angle  between  the  diagonal  of  the  panel 
and  straight  portion  of  the  section  under  consideration  may  be  taken  to  act  as  reinforcement 
in  a  rectangular  direction. 

(k)  Point  of  Inflection. — For  the  purpose  of  making  calculations  of  moments  at  sections 
away  from  the  sections  of  negative  moment  and  positive  moment  already  specified,  the 
point  of  inflection  on  any  line  parallel  to  a  panel  edge  may  be  taken  as  one-fifth  of  the  clear 
distance  on  that  line  between  the  two  sections  of  negative  moment  at  the  opposite  ends  of 
the  panel  indicated  in  paragraph  (e),  of  this  chapter.  For  slabs  having  dropped  panels  the 
coefficient  of  one-fourth  should  be  used  instead  of  one-fifth. 

(1)  *  Arrangement  of  Reinforcement. — The  design  should  include  adequate  provision 
for  securing  the  reinforcement  in  place  so  as  to  take  not  only  the  maximum  moments, 
but  the  moments  at  intermediate  sections.  All  bars  in  rectangular  bands  or  diagonal  bands 
should  extend  on  each  side  of  a  section  of  maximum  moment,  either  positive  or  negative, 
to  points  at  least  twenty  diameters  beyond  the  point  of  inflection  as  defined  herein  or  be 
hooked  or  anchored  at  the  point  of  inflection.  In  addition  to  this  provision  bars  in  diagonal 
bands  used  as  reinforcement  for  negative  moment  should  extend  on  each  side  of  a  line 
drawn  through  the  column  center  at  right  angles  to  the  direction  of  the  band  at  least  a 
distance  equal  to  thirty-five  one-hundredths  of  the  panel  length,  and  bars  in  diagonal  bands 
used  as  reinforcement  for  positive  moment  should  extend  on  each  side  of  a  diagonal  through 
the  center  of  the  panel  at  least  a  distance  equal  to  thirty-five  one-hundredths  of  the  panel 
length;  and  no  splice  by  lapping  should  be  permitted  at  or  near  regions  of  maximum  stress 
except  as  just  described.  Continuity  of  reinforcing  bars  is  considered  to  have  advantages, 
and  it  is  recommended  that  not  more  than  one-third  of  the  reinforcing  bars  in  any  direction 
be  made  of  a  length  less  than  the  distance  center  to  center  of  columns  in  that  direction. 
Continuous  bars  should  not  all  be  bent  up  at  the  same  point  of  their  length,  but  the  zone  in 
which  this  bending  occurs  should  extend  on  each  side  of  the  assumed  point  of  inflection,  and 
should  cover  a  width  of  at  least  one-fifteenth  of  the  panel  length.  Mere  draping  of  the 
bars  should  not  be  permitted.  In  four-way  reinforcement  the  position  of  the  bars  in  both 
diagonal  and  rectangular  directions  may  be  considered  in  determining  whether  the  width 
of  zone  of  bending  is  sufficient. 

(ra)  Reinforcement  at  Construction  Joints. — It  is  recommended  that  at  construction 
joints  extra  reinforcing  bars  equal  in  section  to  20  per  cent  of  the  amount  necessary  to 
meet  the  requirements  for  moments  at  the  section  where  the  joint  is  made  be  added  to  the 
reinforcement,  these  bars  to  extend  not  less  than  50  diameters  beyond  the  joint  on  each 
side. 

(n)  Tensile  and  Compressive  Stresses. — The  usual  method  of  calculating  the  tensile 
and  .compressive  stresses  in  the  concrete  and  in  the  reinforcement,  based  on  the  assump- 
tions for  internal  stresses  given  in  this  chapter,  should  be  followed.  In  the  case  of  the 
dropped  panel  the  section  of  the  slab  and  dropped  panel  may  be  considered  to  act  integrally 
for  a  width  equal  to  the  width  of  the  column-head  section. 

(o)  Provision  for  Diagonal  Tension  and  Shear. — In  calculations  for  the  shearing  stress 
which  is  to  be  used  as  the  means  of  measuring  the  resistance  to  diagonal  tension  stress,  it  is 
recommended  that  the  total  vertical  shear  on  two  column-head  sections  constituting  a 
width  equal  to  one- half  the  lateral  dimensions  of  the  panel,  for  use  in  the  formula  for  deter- 
mining critical  shearing  stresses,  be  considered  to  be  one-fourth  of  the  total  dead  and  live 
load  on  a  panel  for  a  slab  of  uniform  thickness,  and  to  be  three-tenths  of  the  sum  of  the 
dead  and  live  loads  on  a  panel  for  a  slab  with  dropped  panels.  The  formula  for  shearing 

unit  stress  may  then  be  written  v  =  —      —  for  slabs  of  uniform  thickness,  and  v  =     '    . 

bjd  bjd 

for  slabs  with  dropped  panels,  where  W  is  the  sum  of  the  dead  and  live  load  on  a  panel, 
6  is  half  the  lateral  dimension  of  the  panel  measured  from  center  to  center  of  columns,  and 
jd  is  the  lever  arm  of  the  resisting  couple  at  the  section. 

The  calculation  of  what  is  commonly  called  punching  shear  may  be  made  on  the  assump- 
tion of  a  uniform  distribution  over  the  section  of  the  slab  around  the  periphery  of  the 
column  capital  and  also  of  a  uniform  distribution  over  the  section  of  the  slab  around  the 
periphery  of  the  dropped  panel,  using  in  each  case  an  amount  of  vertical  shear  greater  by 
25  per  cent  than  the  total  vertical  shear  on  the  section  under  consideration. 

The  values  of  working  stresses  should  be  those  recommended  for  diagonal  tension 
and  shear  in  the  section  on  "Working  Stresses." 

(p)  Walls  and  Openings. — Girders  or  beams  should  be  constructed  to  carry  walls  and 
other  concentrated  loads  which  are  in  excess  of  the  working  capacity  of  the  lab.  Beams 
should  also  be  provided  in  case  openings  in  the  floor  reduce  the  working  strength  of  the 
slab  below  the  required  carrying  capacity. 

(q)  Unusual  Panels. — The  coefficients,  apportionments,  and  thicknesses  recom- 
mended are  for  slabs  which  have  several  rows  of  panels  in  each  direction,  and  in  which 

252 


the  size  of  the  panels  is  approximately  the  same.  For  structures  having  a  width  of  one, 
two,  or  three  panels,  and  also  for  slabs  having  panels  of  markedly  different  sizes,  an  analysis 
should  be  made  of  the  moments  developed  in  both  slab  and  columns,  and  the  values  given 
herein  modified  accordingly.  Slabs  with  paneled  ceiling  or  with  depressed  paneling  in  the 
floor  are  to  be  considered  as  coming  under  the  recommendations  herein  given. 

(r)  Bending  Moments  in  Columns. — Provision  should  be  made  in  both  wall  columns 
and  interior  columns  for  the  bending  moment  which  will  be  developed  by  unequally  loaded 
panels,  eccentric  loading,  or  uneven  spacing  of  columns.  The  amount  of  moment  to  be 
taken  by  a  column  will  depend  upon  the  relative  stiffness  of  columns  and  slab,  and  com- 
putations may  be  made  by  rational  methods,  such  as  the  principal  of  least  work,  or  of  slope 
and  deflection.  Generally,  the  larger  part  of  the  unequalized  negative  moment  will  be 
transmitted  to  the  columns,  and  the  column  should  be  designed  to  resist  this  bending 
moment.  Especial  attention  should  be  given  to  wall  columns  .and  corner  columns. 

Working  Stresses 

General  Assumptions. — The  following  working  stresses  are  recommended  for  static 
loads.  Proper  allowances  for  vibration  and  impact  are  to  be  added  to  live  loads  where 
necessary  to  produce  an  equivalent  static  load  before  applying  the  unit  stresses  in  propor- 
tioning parts. 

In  selecting  the  permissible  working  stress  on  concrete,  the  designer  should  be  guided 
by  the  working  stresses  usually  allowed  for  other  materials  of  construction,  so  that  all 
structures  of  the  same  class  composed  of  different  materials  may  have  approximately  the 
same  degree  of  safety. 

The  following  recommendations  as  to  allowable  stresses  are  given  in  the  form  of  per- 
centages of  the  ultimate  strength  of  the  particular  concrete  which  is  to  be  used ;  this  ultimate 
strength  is  that  developed  at  an  age  of  twenty-eight  days,  in  cylinders  8  inches  in  diameter 
and  16  inches  long,  of  proper  consistency*  made  and  stored  under  laboratory  conditions. 
In  the  absence  of  definite  knowledge  in  advance  of  construction  as  to  just  what  strength 
may  be  expected,  the  committee  submits  the  following  values  as  those  which  should  be 
obtained  with  materials  and  workmanship  in  accordance  with  the  recommendations  of  this 
report. 

Although  occasional  tests  may  show  higher  results  than  those  here  given,  the  Committee 
recommends  that  these  values  should  be  the  maximum  used  in  design. 

TABLE  OF  COMPRESSIVE  STRENGTHS  OF  DIFFERENT  MIXTURES  OF  CONCRETE 
(In  Pounds  per  Square  Inch) 


Aggregate 
Granite   trap  rock 

l:3t 
3300 

1  :4M  t 
2800 

l:6f 
2200 

l:7Mt 
1800 

l:9t 
1400 

Gravel,  hard  limestone  and  hard  sandstone    .    . 
Soft  limestone  and  sandstone   
Cinders     

3000 
2200 
800 

2500 
1800 
700 

2000 
1500 
600 

1600 
1200 
500 

1300 
1000 

400  . 

NOTE.    For  variations  in  the  moduli  of  elasticity  see  254. 

Bearing. — When  compression  is  applied  to  a  surface  of  concrete  ofvat  least  twice  the 
loaded  area,  a  stress  of  35  per  cent  of  the  compressive  strength  may  be  allowed  in  the 
area  actually  under  load. 

Axial  Compression. — For  concentric  compression  on  a  plain  concrete  pier,  the  length 
of.wnich  does  not  exceed  four  diameters,  or  on  a  column  reinforced  with  longitudinal  bars 
only,  the  length  of  which  does  not  exceed  12  diameters,  22.5  per  cent  of  the  compressive 
strength  may  be  allowed. 

For  other  forms  of  columns  the  stresses  obtained  from  the  ratios  given  in  the  preceding 
section  on  "  Design"  may  govern.  . 

Compression  in  Extreme  Fiber.— The  extreme  fiber  stress  of  a  beam,  calculated  on 
the  assumption  of  a  constant  modulus  of  elasticity  for  concrete  under  working  stresses 
may  be  allowed  to  reach  32.5  per  cent  of  the  compressive  strength.  Adjacent  to  the 
support  of  continuous  beams  stresses  15  per  cent  higher  may  be  used. 

Shear  and  Diagonal  Tension. — In  calculations  on  beams  in  which  the  maximum 
shearing  stress  in  a  section  is  used  as  the  means  of  measuring  the  resistance  to  diagonal 
tension  stress,  the  following  allowable  values  for  the  maximum  vertical  shearing  stress  in 

concrete,  calculated  by  the  method  given  in  formula  on  page  4,  v  =  J-TJ,  are  recommended: 

*  The  materials  should  be  mixed  wet  enough  to  produce  a  concrete  of  such  a  consistency  as  will  flow 
sluggishly  into  the  forms  and  about  the  metal  reinforcement,  and  which,  at  the  same  time,  can  be 
conveyed  from  the  mixer  to  the  forms  without  separation  of  the  coarse  aggregate  from  the  mortar. 
The  quantity  of  water  is  of  the  greatest  importance  in  securing  concrete  of  maximum  strength  and 
density;  too  much  water  is  as  objectionable  as  too  little. 

t  Combined  volume  fine  and  coarse  aggregate  measured  separately. 

253 


(a) — For  beams  with  horizontal  bars  only  and  without  web  reinforcement,  2  per  cent  of 
the  compressive  strength. 

(6) — For  beams  with  web  reinforcement  consisting  of  vertical  stirrups  looped'  about 
the  longitudinal  reinforcing  bars  in  the  tension  side  of  the  beam  and  spaced  horizontally 
not  more  than  one-half  the  depth  of  the  beam;  or  for  beams  in  which  longitudinal  bars  are 
bent  up  at  an  angle  of  not  more  than  45  degrees  or  less  than  20  degrees  with  the  axis  of  the 
beam,  and  the  points  of  bending  are  spaced  horizontally  not  more  than  three-quarters  of  the 
depth  of  the  beam  apart,  not  to  exceed  4)^  per  cent  of  the  compressive  strength. 

(c) — For  a  combination  of  bent  bars  and  vertical  stirrups  looped  about  the  reinforcing 
bars  in  the  tension  side  of  the  beam  and  spaced  horizontally  not  more  than  one-half  of  the 
depth  of  the  beam,  5  per  cent  of  the  compressive  strength. 

(d) — For  beams  with  web  reinforcement  (either  vertical  or  inclined)  securely  attached 
to  the  longitudinal  bars  in  the  tension  side  of  the  beam  in  such  a  way  as  to  prevent  slipping 
of  bar  past  the  stirrup,  and  spaced  horizontally  not  more  than  one-half  of  the  depth  of  the 
beam  in  case  of  vertical  stirrups  and  not  more  than  three-fourths  of  the  depth  of  the  beam 
in  the  case  of  inclined  members,  either  with  longitudinal  bars  bent  up  or  not,  6  per  cent  of 
the  compressive  strength. 

The  web  reinforcement  in  case  any  is  used  should  be  proportioned  by  using  two-thirds 
of  the  external  vertical  shear  in  formulas  (a)  and  (6)  on  page  4.  The  effect  of  longitu- 
dinal bars  bent  up  at  an  angle  of  from  20  to  45  degrees  with  the  axis  of  the  beam  may 
be  taken  at  sections  of  the  beam  in  which  the  bent  up  bars  contribute  to  diagonal 
tension  resistance  (see  "Diagonal  Tension  and  Shear,"  page  245)  as  reducing  the 
shearing  stresses  to  be  otherwise  provided  for.  The  amount  of  reduction  of  the  shearing 
stress  by  means  of  bent  up  bars  will  depend  upon  their  capacity,  but  in  no  case  should  be 
taken  as  greater  than  4  %  per  cent  of  the  compressive  strength  of  the  concrete  over  the 
effective  cross-section  of  the  beam.*  The  limit  of  tensile  stress  in  the  bent  up  por- 
tion of  the  bar  calculated  by  formula  (6)  on  page  4,  using  in  this  formula  an  amount  of  total 
shear  corresponding  to  the  reduction  in  shearing  stress  assumed  for  the  bent  up  bars, 
may  be  taken  as  specified  for  the  working  stress  of  steel,  but  in  the  calculations  the 
stress  in  the  bar  due  to  its  part  as  longitudinal  reinforcement  of  the  beam  should  be 
considered.  The  stresses  in  stirrups  and  inclined  members  when  combined  with  bent 
up  bars  are  to  be  determined  by  finding  the  amount  of  the  total  shear  which  may  be 
allowed  by  reason  of  the  bent  up  bars,  and  subtracting  this  shear  from  the  total  external 
vertical  shear.  Two-thirds  of  the  remainder  will  be  the  shear  to  be  carried  by  the  stirrups, 
using  formulas  (a)  or  (6)  on  page  4. 

Where  punching  shear  occurs,  provided  the  diagonal  tension  requirements  are  met, 
a  shearing  stress  of  6  per  cent  of  the  compressive  strength  may  be  allowed. 

Bond. — The  bond  stress  between  concrete  and  plain  reinforcing  bars  may  be  assumed 
at  4  per  cent  of  the  compressive  strength,  or  2  per  cent  in  the  case  of  drawn  wire.  In  the 
best  types  of  deformed  bar  the  bond  stress  may  be  increased,  but  not  to  exceed  5  per  cent  of 
the  compressive  strength  of  the  concrete. 

Reinforcement. — The  tensile  or  compressive  stress  in  steel  should  not  exceed  16,000 
pounds  per  square  inch. 

In  structural  steel  members  the  working  stresses  adopted  by  the  American  Railway 
Engineering  Association  are  recommended. 

Modulus  of  Elasticity. — The  value  of  the  modulus  of  elasticity  of  concrete  has  a  wide 
range,  depending  on  the  materials  used,  the  age,  the  range  of  stresses  between  which  it  is 
considered,  as  well  as  other  conditions.  It  is  recommended  that  in  computations  for  the 
position  of  the  neutral  axis,  and  for  the  resisting  moment  of  beams  and  for  compression 
of  concrete  in  columns,  it  be  assumed  as: 

(a) — One-fortieth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  not  more 
than  800  pounds  per  square  inch. 

(6) — One-fifteenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater 
than  800  pounds  per  square  inch. 

(c) — One-twelfth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater 
than  2,200  pounds  per  square  inch,  and  less  than  2,900  pounds  per  square  inch. 

(d) — One-tenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater 
than  2,900  pounds  per  square  inch. 

Although  not  rigorously  accurate,  these  assumptions  will  give  safe  results.  For  the 
deflection  of  beams  which  are  free  to  move  longitudinally  at  the  supports,  in  using  formulas 
for  deflection  which  do  not  take  into  account  the  tensile  strength  developed  in  the  concrete, 
a  modulus  of  one-eighth  of  that  of  steel  is  recommended. 


254 


AMERICAN  CONCRETE  INSTITUTE  RECOMMENDATIONS* 

1.  Conditions. — All   reinforced-concrete  construction  shall   be  designed   to  meet  the 
conditions  of  loading  (including  bending  in  columns)  without  stressing  the  materials  used 
beyond  the  safe  working  stresses  specified. 

2.  Dead-Loads. — The  dead-loads  shall  be  the  weight  of  the  permanent  structure.     The 
weight  of  reinforced  stone,  gravel  or  slag  concrete  shall  be  taken  as  144  Ib.  per  cu.  ft.; 
the  weight  of  cinder  concrete  as  100  Ib.  per  cu.  ft. 

3.  Live-Loads. — The  live-load  shall  be  the  working  or  variable  load  for  which  the 
structure  is  designed. 

4.  Reduction  of  Loads. — All  parts  of  a  structure  shall  be  designed  to  carry  safely  the 
entire  combined  dead-  and  live-loads  with  the  exception  that  the  loads  on  columns  and 
foundations  may  be  reduced  by  considering  that  columns  in  top  story  carry  the  total  live- 
and  dead-load  above  them;  columns  in  next  to  top  story  carry  the  total  dead-load  and 
eighty-five  (85)  per  cent  of  the  total  live-load  above;  columns  in  the  next  lower  story,  the 
total  dead-load  and  eighty  (80)  per  cent  of  the  total  live-load  above:  and  thus  on  downward 
reducing  at  each  story  the  percentage  of  total  live-loads  carried,  by  5,  until  a  reduction  of 
fifty   (50)    per  cent  is  reached.     The  columns  in  this  and  in  every  story  below  this  point 
shall  be  proportioned  to  carry  the  total  dead-load  and  at  least  fifty  (50)  per  cent  of  the 
total  live-load  of  all  the  floors  and  roofs  above  them. 

For  warehouses  the  increment  of  reduction  per  story  shall  be  2^  per  cent  instead  of  5  per 
cent. 

5.  General  Assumptions. — As  a  basis  for  calculations  for  the  strength  of  reinforced- 
concrete  construction  the  following  assumptions  shall  be  made: 

(a)   Calculations  shall  be  made  with  reference  to  working  stresses  and  safe  loads 
rather  than  with  reference  to  ultimate  strength  and  ultimate  loads. 
(6)    A  plane  section  before  bending  remains  plane  after  bending. 

(c)  The  modulus  of  elasticity  of  concrete  in  compression  within  the  usual  limits  of 
working  stresses  is  constant. 

(d)  In  calculating  the  moment  of  resistance  of  beams,  the  tensile  stresses  in  the 
concrete  are  neglected. 

(e)  Perfect    adhesion   is    assumed    between    concrete    and    reinforcement.     Under 
compressive  stresses  the  two  materials  will,  therefore,  be  stressed  in  proportion  to  their 
moduli  of  elasticity. 

(/)    The  ratio  of  the  modulus  of  elasticity  of  concrete  shall  be  taken  as  follows : 

1.  One-fortieth  that  of  steel  when  the  strength  of  the  concrete  is  taken  as  not  more 

than  eight  hundred  (800)  Ib.  per  sq.  in. 
2    One-fifteenth  that  of  steel  when  the  strength  of  the  concrete  is  taken  as  greater 

than  twelve  hundred   (1200)  Ib.  per  sq.  in.  or  less  than  twenty-two  hundred 

(2200)  Ib.  per  sq.  in. 

3.  One-twelfth  that  of  steel  when  strength  of  the  concrete  is  taken  as  greater  than 
twenty- two  hundred  (2200)  Ib.  per  sq.  in.  or  less  than  thirty- three  hundred  (3300) 
Ib.  per  sq.  in. 

4.  One-tenth  that  of  steel  when  the  strength  of  the  concrete  is  taken  as  greater  than 
thirty-three  hundred  (3300)  Ib.  per  sq.  in. 

6.  Strength  of  Materials. — The  ultimate  strength  of  concrete  shall  be  that  developed  at 
an  age  of  28  days,  in  cylinders  8  in.  in  diameter  and  16  in.  in  length  or  6  in.  in  diameter  and 
12  in.  in  length,  of  the  consistency  and  proportions  to  be  used  in  the  work,  made  and  stored 
under  laboratory  conditions,  but  in  no  case  shall  the  values  exceed  those  allowed  in  the  table 
below.     In  the  absence  of  definite  knowledge  in  advance  of  construction  as  to  just  what 
strength  may  be  developed,  the  following  values  may  be  used: 

*  Passed  by  letter-ballot  of  the  Institute,  April  17,  1920. 

'     255 


TABLE  OF  STRENGTHS  OF  DIFFERENT  MIXTURES 

Proportion  of  cement  to  aggregate 

Aggregate                                                                      1:3*        1:4>2*          1:6*  1:7^*        1:9* 
For  stone,  gravel  or  slag  with  water-cement 

ratiot  of : 0.8           0.9           1.0  1.11          1.22 

Strength  of  concrete 3000         2500         2000  1600          1300 

Cinders SDO           700           600  500           400 

7.  Safe  Working  Stresses. — Reinforced-concrete  structures  shall  be  so  designed  that  the 
stresses,  figured  in  accordance  with  these  regulations,  in  pounds  per  square  inch,  shall  not 
exceed  the  following: 

(a)  Extreme  fiber  stress  in  concrete  in  compression  37^  per  cent  of  the  compressive 
strength  specified  in  Section  6.  Adjacent  to  the  support  of  continuous  members,  41  per 
cent  provided  the  member  frames  into  a  mass  of  concrete  projecting  at  least  50  per  cent 
of  the  least  dimension  of  the  member  on  all  sides  of  the  compression  area  of  the  member. 

(6)  Concrete  in  direct  compression  25  per  cent  of  the  compressive  strength  specified 
in  Section  6. 

(c)  Shearing  stress  in  concrete  when  main  steel  is  not  bent  and  when  steel  is  not 
provided  to  resist  diagonal  tension,  as  specified  in  Section  10. 

(d)  Where  punching  shear  occurs,  provided  the  diagonal  tension  requirements  are 
met,  a  shearing  stress  as  specified  in  Section  10  will  be  allowed. 

(e)  Vertical  shearing  stresses,  as  specified  in  Section  10. 

(/)  Bond  stress  between  concrete  and  plain  reinforcing  bars — 4  per  cent  of  the 
compressive  strength. 

(fir)  Bond  stress  between  concrete  and  approved  deformed  bars — 5  per  cent  of  the 
compressive  strength. 

(ft)  Compression  applied  to  a  surface  of  concrete  of  at  least  twice  the  loaded  area, 
a  stress  of  50  per  cent  of  the  compressive  strength  shall  be  allowd  over  the  area  actually 
under  load. 

(?')  Tensile  stress  in  steel — 16,000  Ib.  per  sq.  in.,  except  that  for  steel  having  an 
elastic  limit  of  at  least  50,000  Ib.,  a  working  stress  of  18,000  Ib.  per  sq.  in.  will  be 
allowed. 

8.  Girder,   Beam,   and   Slab   Construction. — In  determining  the  bending  moment  in 
slabs,  beams  and  girders,  the  load  carried  by  the  member  shall  include  both  the  dead-  and 
the  live-loads. 

The  span  of  the  member  shall  be  the  distance  center  to  center  of  supports,  but  not  to 
exceed  the  clear  span  plus  the  depth  of  the  member,  except  that  for  continuous  or  fixed 
members  framing  into  other  reinforced-concrete  members  the  clear  span  may  be  used. 

For  continuous  members  supported  upon  brackets  making  an  angle  of  not  more  than 
45  degrees  with  the  vertical,  and  having  a  width  not  less  than  the  width  of  the  member 
supported,  the  span  shall  be  the  clear  distance  between  brackets  plus  one-half  the  total 
depth  of  the  member. 

If  the  brackets  make  a  greater  angle  than  45  degrees  with  the  vertical,  only  that  portion 
of  the  bracket  within  the  45  degrees  slope  shall  be  considered.  Maximum  negative  mo- 
ments are  to  be  considered  as  existing  at  the  end  of  the  span  as  here  defined. 

~WJ 
For  members  uniformly  loaded  the  bending  moment  shall  be  assumed  as  -=r-  >  where 

b 

W  =  total  load;  L  =  span;  and  F  =  8  for  members  simply  supported,  10  for  both 
negative  and  positive  bending  moment  for  members  restrained  at  one  end  and  simply 
supported  or  partially  restrained  at  the  other,  and  12  for  both  negative  and  positive  bend- 
ing moment  for  members  fixed  or  continuous  at  both  supports.  The  above  bending  mo- 
ments for  continuous  members  apply  only  when  adjacent  spans  are  approximately  equal. 
A  special  condition  of  loading  to  be  reduced  to  equivalent  uniformly  distributed  loading 
in  accordance  with  approved  engineering  practice.  For  members  having  one  end  simply 
supported  or  partially  restrained,  at  least  fifty  (50)  per  cent  of  the  tension  reinforcement 
required  at  center  of  span  shall  be  bent  up  and  adequately  anchored  to  take  bending  moment 
at  exterior  support. 

At  the  ends  of  continuous  beams,  the  amount  of  negative  moment  which  will  be  devel- 
oped in  the  beam  will  depend  on  the  condition  of  restraint  or  fixedness,  and  this  will  depend 

on  the  form  of  construction  used.     In  the  ordinary  cases  a  moment  of  ,--  may  be  taken: 

ID 

for  small  beams  running  into  heavy  columns  this  should  be  increased  but  not  to  exceed  ^ 

*  Total  volume  of  fine  and  coarse  aggregate,  measured  separately, 
t  Water-Cement  Ratio  =  Ratio  of  water  to  cement  by  volume. 

256 


9.  Slabs. — The  main  tensile  reinforcement  shall  not  be  farther  apart  than  two  times 
the  thickness  of  the  slab.     For  slabs  designed  to  span  one  way,  steel  having  an  area  of  at 
least  two-tenths  of  one  per  cent  (0.2  %)  of  section  of  slab  shall  be  provided  transverse  to 
main  reinforcement,  and  this  transverse  reinforcement  shall  be  further  increased  in  the  top 
of  the  slab  over  girders  to  prevent  cracking,  and  the  main  steel  in  slabs  parallel  and  adjacent 
to  girders  may  be  reduced  accordingly.     Where  openings  are  left  through  slabs,  extra 
reinforcement  shall  be  provided  to  prevent  local  cracks  developing.     This  reinforcement 
shall  in  no  case  be  less  than  Y±  sq.  in.  in  section  and  must  be  securely  anchored  at  ends. 
Floor  finish  when  placed  monolithic  may  be  considered  part  of  the  structural  section. 

Where  adequate  bond  and  shearing  resistance  between  slab  and  web  of  beam  is  provided, 
the  slab  may  be  considered  as  an  integral  part  of  the  beam,  but  its  effective  width  shall  not 
exceed  on  either  side  of  the  beam  one-sixth  of  the  span  length  of  the  beam  nor  be  greater 
than  six  times  the  thickness  of  the  slab  on  either  side  of  the  beam,  nor  greater  than  one-half 
of  the  distance  between  beams  on  either  side,  the  measurements  being  taken  from  edge  of 
web. 

10.  Shear  and  Diagonal  Tension. — (a)  The  notation  used  in  this  section  is  as  follows: 

V  =  total  vertical  shear  at  any  section. 
V  =  vertical  shear  carried  by  the  web  reinforcement.  • 

v  =  V/bjd  =  Unit  vertical  shearing  stress. 

d  =  depth  from  compressive  face  to  c.  g.  of  tensile  steel  in  inches. 

b  =  breadth  of  beam. 

bf  =  breadth  of  stem  of  T-beam  or  web  of  I-beam. 
As  =  area  of  longitudinal  steel. 
Av  =  area  of  shear  steel  in  section  of  beam  considered. 

j  =  ratio  of  lever  arm  of  resistance  couple  to  depth  d. 

p  =  Ag/bd  =  Longitudinal  steel  ratio. 

r  =  Av/ba  =  Shear  steel  ratio. 

a  =  spacing  of  shear  steel  measured  perpendicular  to  its  direction. 
fe'  =  ultimate  strength  of  concrete  cylinders  at  28  days  (or  at  time  of  test  in  considering 
test  data). 

/„  =  tensile  stress  in  web  reinforcement. 

Except  where  v  is  noted  as  the  unit  punching  shearing  stress,  it  is  used  as  a  shearing 
stress  index  governing  the  v  alue  of  the  diagonal  tension  in  the  web  as  is  the  present  common 
practice. 

(6)  All  allowances  for  design  unit  shearing  stresses  in  the  following  sections  are  predicated 
on  proper  design  of  the  longitudinal  reinforcement  to  effectively  resist  all  positive  and 
negative  moments,  as  prescribed  in  other  sections  of  these  standards.  Wherever  web 
reinforcement  is  used  it  must  be  adequately  anchored  at  both  ends. 

(c)  Members  with  Web  Reinforcement. — When  adequate  mechanical  anchorage  of  both 
web  and  longitudinal  rods  is  provided,  the  concrete  may  be  figured  to  carry  a  unit  vertical 
shearing  stress  equal  to  0.025/c'  and  the  remainder  of  the  shear  shall  be  carried  by  web  bars 
designed  according  to  the  formula: 

A     -V'a 

~m 

Properly  anchored  bent-up  longitudinal  bars  may  be  considered  as  web  reinforcement. 
The  maximum  unit  shearing  stress  shall  not  exceed  0.12/c'  in  any  case. 

(d)  When  adequate  mechanical  anchorage  of  the  longitudinal  rods  as  defined  in  the  next 
paragraph  is  not  provided,  the  maximum  unit  shearing  stress  shall  not  exceed    0.06/c', 
of  which  0.02//  may  be  considered  to  be  taken  by  the  concrete  and  the  remainder  of  the 
shear  taken  by  the  web  bars  designed  as  above.     Web  rods  must  be  adequately  anchored  in 
all  cases. 

(e)  Adequate   mechanical   anchorage   of   the    bottom   longitudinal   steel   for   positive 
moments  shall  consist  of  carrying  the  reinforcement  a  sufficient  distance  beyond  the  point 
of  inflection  to  develop  the  assumed  tension  in  the  reinforcement  at  the  point  of  inflection 
by  bond  between  the  end  of  the  bar  and  the  point  of  inflection  of  the  member  (never  to  a 
less  distance  than  one  inch  from  the  center  of  the  support  or  in  case  of  wide  supports  to  not 
less  than  12  in.  of  embedment  in  the  support),  or  of  bending  the  end  of  the  bars  over  the 
support  to  a  half  circle  of  diameter  not  less  than  8  times  the  diameter  of  the  bar,  or  by  any 
device  that  will  transmit  the  tension  on  the  bar  to  the  concrete  over  the  support  at  a 
compressive  stress  of  not  over  0.50/c'.     The  tension  in  the  bar,  at  the  point  of  inflection 
to  be  resisted  by  the  anchorage,  shall  be  taken  for  this  computation  as  not  less  than  one- 
third  of  the  maximum  safe  tension  in  the  bar.     Reinforcement  for  negative  moment  shall 
be  thoroughly  anchored  at  the  support  and  extend  into  the  span  a  sufficient  distance  to 
adequately  provide  for  negative  tension  by  bond.     Simply  supported  beams  shall  have  the 
longitudinal  steel  anchored  by  hooks  of  diameter  specified  above  or  by  an  equivalent  anchor- 

257 


age,  the  tensile  stress  at  the  edge  of  the  support  being  taken  as  one-third  of  the  maximum 
safe  tension  in  the  bar.     (Figs.  1,  2  and  3.) 

(/)  Anchorage  of  the  web  steel  shall  consist  of  continuity  of  the  web  member  with  the 
longitudinal  member,  or  of  carrying  the  web  member  about  at  least  two  sides  of  a  longitudi- 
nal bar  at  both  ends,  or  of  carrying  the  web  member  about  at  least  two  sides  of  a  longitudinal 
member  at  one  end  and  making  a  half  circular  hook  at  the  other  end  of  a  diameter  not  less 
than  eight  times  the  diameter  of  the  web  rod.  In  all  cases,  the  bent  ends  of  web  bars  shall 
extend  at  least  eight  diameters  below  or  above  the  point  of  extreme  height  or  depth  of  the 


"^JT        ^ 

_^L_ 


Steel  from    %&$(£'*   Vertical  stirrups 
adjacent  only 

span  not  shown 

FIG.  1, 


Bent  up  rods  i-j 
and  vertical  stirrups 


Steel  from    % 
adjacent 
span  not  shown 


Bent  up  bars  and  inclined  stirrups 
FIG.  2. 


Plate  must  be  rigid- 
ly connected  to  rod 


FIG.  3. 


:;*;>'.,:  >•>•';•£ 

*  '      ^    \ 
-  •$ 

po  * 

P5l 

Hook  must  engage 
a  substantial  block 
of  concrete 

'  .  4 
_'   A  . 

**Gd           "'This  dimension  limited 
by  bond  value  unless  wffb 
*  ^                 ste*l  is  integral  with 
longitudinal  steel 

;••:.•?•: 

W 

•  '••'•'•  4 

FIG.  4. 


on  this  section  must  not  exceed  .02  f, 
unless  steel  is  provided  in  top  of  beam  at  support 

FIG.  5. 


bar.  In  case  the  end  anchorage  is  not  in  bearing  on  other  reinforcing  steel,  the  anchorage 
shall  be  such  as  to  engage  an  adequate  amount  of  concrete  to  prevent  the  bar  from  pulling 
off  a  portion  of  the  concrete.  In  all  cases  the  stirrups  shall  be  carried  as  close  to  the  upper 
and  lower  surfaces  as  fireproofing  requirements  will  permit.  The  size  of  web  reinforcing 
bars  which  are  not  either  a  part  of  the  longitudinal  steel  or  welded  thereto  shall  be  such  that 
not  less  than  two-fifths  of  the  maximum  design  tensile  stress  in  the  bar  may  be  developed 
at  design  bond  stresses  in  a  length  of  rod  equal  to  0.4d.  This  condition  is  satisfied  for  plain 

258 


round  stirrups  when  the  diameter  of  the  bar  does  not  exceed  d/50.  The  balance  of  the 
tensile  stress  in  the  bar  may  be  considered  as  taken  by  adequate  end  anchorage  as  specified 
above.  (Fig.  4.) 

(0)  Beams  in  which  no  longitudinal  reinforcement  is  provided  in  the  upper  portion  of  the 
beam  adjacent  to  the  support  and  in  which  the  ends  of  the  beam  are  built  monolithic  with 
other  parts  of  the  concrete  structure,  shall  not  carry  a  unit  shearing  stress  in  excess  of 
0.02//,  regardless  of  amount  of  web  reinforcement  provided.  (Fig.  5.) 

(A)  When  the  shear  reinforcement  consists  of  bars  bent  up  at  an  angle  so  as  to  rein- 
force all  sections  of  the  beam  in  which  the  unit  shearing  stress  exceeds  0.02/c'  the  design 
may  be  made  as  follows: 

Atfv    =  V  sec  a. 

Where  Av    =  area  of  bent-up  shear  bars. 
/„    =  stress  in  bent-up  shear  bars. 
V'    =  total   shear   at  end  of  span  as  prescribed  for  moment  less  the  shearing 

resistance  of  the  concrete  at  a  unit  stress  of  0.02/c'  over  the  area  b'jd. 
a  =  angle  between  bent-up  rod  and  the  vertical.     (F^g.  6.) 


FIG.  6. 


The  maximum  unit  shearing  stress  shall  not  exceed  0.06  fcf  with  this  arrangement  of  web 
steel  and  the  longitudinal  steel  shall  be  adequately  anchored  as  defined  above  in  all  cases. 

(i)  In  case  the  web  reinforcement  consists  solely  of  inclined  shear  bars  the  first  bent  bar 
shall  bend  downward  from  the  plane  of  the  upper  reinforcement  directly  over  or  within  the 
edge  of  the  support. 

0')  Where  additional  web  reinforcement  is  provided  the  same  may  be  figured  in  accord- 
ance with  Section  10  (c).  The  total  shearing  resistance  of  the  beam  shall  be  taken  as  the 
sum  of  the  resistances  under  Section  10  (c)  and  10  (h). 

(k)  Beams  without  Web  Reinforcement. — When  the  longitudinal  steel  is  not  fully  an- 
chored, as  prescribed  above,  the  unit  shearing  stress  shall  not  exceed  0.02//.  When  the 
longitudinal  steel  is  fully  anchored,  as  prescribed  above,  the  unit  shearing  stress  shall  not 
exceed  0.03//. 

(I)  Critical  Section  for  Shear  in  Beams. — The  critical  section  for  shear  as  governing 
diagonal  tension  shall  be  taken  at  a  distance  not  greater  than  one-half  the  effective  depth  of 
the  beam  O^d),  from  the  end  of  the  span  as  prescribed  for  moment. 


C.G. 


Shear  governing  diagonal  tension 
Critical  sections   (IJ  following  per- 
iphery of  drop  panel,  and  (2)  sur- 
face of  frustum  of  cone  thru  e> 
of  column  capital;  base 


Punching  shear:— 
-  Critical  section  follows  per- 
iphery of  column  capital 


The  effective  depth  of  the  critical  section  for  shear  as  governing  diagonal  tension  shall 
be  taken  as  the  depth  jd  of  the  beam  in  the  plane  of  the  critical  section. 

The  breadth  of  the  critical  section  shall  be  the  full  breadth  of  rectangular  beams  or  the 
breadth  of  the  stem  of  T-beams  or  the  thickness  of  the  web  in  beams  of  I  section. 

(m)  TUe  and  Concrete  Joist  Construction. — The  shearing  stresses  in  tile  and  concrete 
joist  construction  shall  not  exceed  those  in  beams  or  slabs  of  similar  reinforcement.  The 
breadth  of  the  effective  section  for  shear,  as  governing  diagonal  tension,  may  be  taken  as 
the  thickness  of  the  concrete  joist  plus  one-half  the  thickness  of  the  vertical  webs  of  the 
tile,  provided  that  the  joints  in  one  row  come  opposite  the  centers  of  tile  in  adjoining  rows 
on  either  side. 

Where  the  tile  joints  are  not  staggered,  only  the  concrete  joists  may  be  considered 
effective  in  resisting  shear. 

259 


(n)  Flat-slab  Construction. — In  flat-slab  construction  where  a  drop  panel  is  used  ad- 
joining the  column,  the  shearing  stress,  as  governing  diagonal  tension,  figured  on  the  jd 
depth  on  a  vertical  section  along  the  periphery  of  the  drop,  shall  not  exceed  0.03/c'.  (See 
Fig.  7.) 

(o)  In  flat-slab  construction,  with  or  without  drop  panels,  the  shearing  stress,  as  govern- 
ing diagonal  tension,  figured  between  the  compression  face  of  the  slab  or  drop  and  the  level 
of  the  center  of  gravity  of  the  reinforcing  steel,  on  the  surface  of  the  frustum  of  a  cone  or 
pyramid  passing  through  the  periphery  of  the  column  capital  and  having  a  base  angle  of 
45  degrees,  shall  not  exceed  0.035/c'. 

(p)  Footings. — In  footings  carrying  a  single  column  or  load,  the  shearing  stress,  as 
governing  diagonal  tension,  figured  between  the  level  of  the  centroid  of  the  compressive 
stresses  and  the  level  of  the  center  of  gravity  of  the  reinforcing  steel  on  the  surface  of  the 
frustum  of  a  cone  or  pyramid  passing  through  the  base  of  the  supported  column  or  loaded 
member  and  having  a  base  angle  of  45  degrees  the  unit  stresses  shall  not  exceed  those  in 
beams  without  web  reinforcement.  Especial  attention  shall  be  given  to  bond  in  footings. 
The  total  vertical  shear  on  this  section  shall  be  taken  as  the  upward  pressure  on  the  area 
of  the  footing  outside  the  base  of  this  section. 

(q)  If  adequate  anchorage  is  provided  for  the  tensile  steel  arid  adequately  anchored 
web  reinforcement  is  also  provided  such  web  reinforcement  may  be  figured  in  accordance 
with  the  formula  given  in  Section  10  (c)  above.  Such  calculations  may  be  made  for  vertical 
sections  concentric  with  the  supported  column. 

(r)  For  footings  supporting  two  or  more  columns,  the  shearing  stresses  shall  be  figured 
as  for  beams  or  slabs. 

(s)  Arrangement  of  Web  Reinforcement. — The  spacing  of  web  reinforcement  as  measured 
perpendicular  to  their  direction  shall  not  exceed  3d/4  in  any  case  where  web  reinforcement 
is  necessary.  Where  vertical  stirrups  or  web  members  inclined  less  than  30  degrees  to  the 


Shear  governing  diagonal  tension :-}  \    Punching  shear  :- 
Critical  section  follows  periphery-'  ^- Critical 'section  follows  periphery 

of  supported  portion  at  top  of  of  supported  portion, 

footing;  base  angle  45° 


FIG.  8. 


vertical  are  used,  the  spacing  shall  not  exceed  d/2.  When  the  unit  shearing  stress  exceeds 
0.06/c'  the  spacing  of  the  web  reinforcement  shall  not  exceed  d/2  in  any  case,  nor  d/3  for 
vertical  stirrups  or  web  steel  inclined  less  than  30  degrees  with  the  vertical. 

The  first  vertical  stirrup  shall  be  placed  not  farther  than  d/2  from  the  face  of  the 
support  in  any  case.  The  first  inclined  stirrup  or  bent-up  rod  shall  reach  the  level  of  the 
upper  longitudinal  steel  at  a  distance  not  greater  than  d/2  from  the  edge  of  the  support  if 
the  bottom  longitudinal  steel  is  adequately  anchored  and  at  the  edge  of  the  web  support  if 
the  longitudinal  steel  is  not  anchored.  Web  members  may  be  placed  at  any  angle  between 
0  and  60  degrees  with  the  vertical,  provided  that,  if  inclined,  they  shall  be  inclined  in  the 
proper  direction  to  take  tension,  rather  than  compression,  in  the  web. 

(t)  Punching  Shear. — Punching  shear  shall  be  figured  on  a  vertical  section  through 
the  periphery  of  the  smaller  member.  The  unit  shearing  stress  in  punching  shear,  figured 
on  the  full  depth  d  to  the  center  of  gravity  of  the  reinforcement,  shall  not  exceed  0.1/c'. 

(u)  When  the  depth  of  the  supported  or  supporting  member  is  less  than  one-fifteenth  of 
the  span  in  the  case  of  beams  or  slabs,  or  less  than  one-third  of  the  overhang  in  the  case  of 
cantilevers  (including  footings),  the  unit  shearing  stress  in  punching  shear  shall  not  exceed 
0.06/c'. 

11.  Tile  and  Joist  Floors. — Wherever  floors  are  built  with  a  combination  of  tile  or 
other  fillers  between  reinforced-concrete  joists,  the  following  rules  regarding  the  dimensions 
and  methods  of  calculations  of  construction  shall  be  observed: 

(a)  Wherever  a  portion  of  the  slab  above  the  fillers  is  considered  as  acting  as  a  T-beam 
section,  the  slab  portion  must  be  cast  monolithic  with  the  joist  and  have  a  minimum  thick- 
ness of  two  (2)  inches. 

(6)  Wherever  porous  fillers  are  used  which  will  absorb  water  from  the  concrete,  oare 
must  be  taken  thoroughly  to  saturate  same  before  concrete  is  placed. 

260 


(c)  All  regulations  given  above  for  beam  and  girder  floors  shall  apply  to  tile  and  joist 
floors. 

(d)  The  sections  of  fillers  shall  be  together  and  all  joints  reasonably  tight  before  concrete 
is  placed. 

12.  Flat -slab  or  Girderless  Floors, — Continuous  flat-slab  floors,  reinforced  with  steel 
rods  or  mesh  and  supported  on  spaced  columns  in  orderly  arrangement,  shall  conform  to  the 
following  requirements: 


FIG.  9. 

(a)  Notation  and  Nomenclature. — In  the  formula  let 

w  =  total  dead-and  live-load  in  pounds  per  square  foot  of  floors. 

l\  ='span  in  feet  center  to  center  of  columns  parallel  to  sections  on  which  moments 

are  considered. 
lz  =  span  in  feet  center  to  center  of  columns  perpendicular  to  sections  on  which 

moments  are  considered. 

C    =  average  diameter  of  column  capital  in  feet  at  plane  where  its  thickness  is  1%  in. 
q    =  distance  from  center  line  of  the  capital  to  the  center  of  gravity  of  the  periphery 

of  the  half  capital  divided  by  %c.     For  round  capitals  q  may  be  considered 

as  two-thirds  and  for  square  capitals  as  three-quarters. 
t     =  total  slab  thickness  in  inches. 
L  =  average  span  in  feet  center  to  center  of  columns,  but  not  less  than  0.9  of  the 

greater  span. 


(a)  Drop  construction 


(f>s  Cop  construct  kjf  > 


£7 


\_i_/   i- 

TF-- - - 

(c)  Poneifed  ceiling  consfPtocficn 
FlG.  10. 


The  column  head  section,  mid  section,  outer  section,  and  inner  section  are  located  and 
dimensioned  as  shown  in  Fig.  9.  Corresponding  moments  shall  be  figured  on  similar 
sections  at  right  angles  to  those  shown  in  Fig.  9. 

(b)  Structural  Variations. — Flat-slab  floors  may  be  built  with  or  without  caps,  drops  or 
paneled  ceilings.  These  terms  are  illustrated  in  Fig.  10. 

Where  caps  are  employed  they  shall  be  considered  a  part  of  the  columns  and  the  column 

261 


capital  dimension  c  shall  be  found  by  extending  the  lines  of  the  capital  to  an  intersection 
with  the  plane  of  the  under  surface  of  the  slab  as  indicated  in  Fig.  10&.  The  cap  shall  be 
large  enough  to  enclose  this  extension  of  the  capital  lines. 

The  column  capital  profile  shall  not  fall  at  any  point  inside  an  inverted  cone  drawn,  as 
shown  in  Fig.  10a,  from  the  periphery  of  the  designed  capital  of  diameter  c  and  with  a  base 
angle  of  45  degrees.  The  diameter  of  the  designed  capital  c  shall  be  taken  where  the  verti- 
cal thickness  of  the  column  capital  is  at  least  1%  in. 

The  drop,  where  used,  shall  not  be  less  than  0.3  L  in  width. 

Where  paneled  ceilings  are  used  the  paneling  shall  not  exceed  one-half  of  the  slab 
thickness  in  depth  and  the  dimension  of  the  paneling  shall  not  exceed  0.8  of  the  panel  dimen- 
sion. (See  Fig.  lOo.) 

(c)  Slab  Thickness. — The  slab  thickness  shall  not  be  less  than  t  =  0.02L  ^/w  +  1  in. 

In  no  case  shall  the  slab  thickness  be  less  than  ^  2-^  f °r  floor  slabs  nor  less  than  Y±  oL  for 
roof  slabs. 

(d)  Design  Moments. — The  numerical  sum  of  the  positive  and  negative  moments  in  foot 
pounds   shall   not   be  less   than  0.09wli(l«  —  gc)2.     Of  this  total  amount  not  less  than  40 
per  cent  shall  be  resisted  in  the  column  head  sections.     Where  a  drop  is  used,  not  less  than 
50  per  cent  shall  be  resisted  in  the  column  head  sections. 

Of  the  total  amount  not  less  than  10  per  cent  shall  be  resisted  in  the  mid  section. 

Of  the  total  amount  not  less  than  18  per  cent  shall  be  resisted  in  the  outer  section. 

Of  the  total  amount  not  less  than  12  per  cent  shall  be  resisted  on  the  inner  sections. 

The  balance  of  the  moment  shall  be  distributed  between  the  various  sections  as  required 
by  the  physical  details  and  dimensions  of  the  particular  design  employed. 

(c)  Exterior  Panels. — The  negative  moments  at  the  first  interior  row  of  columns  and  the 
positive  moments  at  the  center  of  the  exterior  panel  on  sections  parallel  to  the  wall,  shall 
be  increased  20  per  cent  o\er  those  specified  above  for  interior  panels.  If  girders  are  not 
provided  long  the  column  line,  the  reinforcement  parallel  to  the  wall  for  negative  moment  in 
the  column  head  section  and  for  positive  moment  in  the  outer  section  adjacent  to  the  wall, 
shall  be  altered  in  accordance  with  the  change  in  the  value  of  c.  The  negative  moment  on 
sections  at  the  wall  and  parallel  thereto  should  be  determined  by  the  conditions  of  restraint, 
but  must  never  be  taken  less  than  80  per  cent  of  those  for  the  interior  panels. 

(/)  Reinforcement. — In  the  calculation  of  moments  all  the  reinforcing  bars  which  cross 
the  section  under  consideration  and  which  fulfill  the  requirements  given  under  "Arrange- 
ment of  Reinforcement"  may  be  used.  For  a  column  head  section  reinforcing  bars  parallel 
to  the  straight  portion  of  the  section  do  not  contribute  to  the  negative  resisting  moment 
for  the  column  head  section  in  question.  The  sectional  area  of  bars,  crossing  the  section 
at  an  angle,  multiplied  by  the  sine  of  the  angle  between  these  bars  and  the  straight  portion 
of  the  section  under  consideration  may  be  taken  to  act  as  reinforcement  in  a  rectangular 
direction.  Calculations  for  shearing  stress  shall  be  made  in  accordance  with  Section  10. 

(g)  Point  of  Inflection. — For  the  purpose  of  making  calculations  of  moment  at  sections 
away  from  the  sections  of  negative  moment  and  positive  moment  already  specified,  the 
point  of  inflection  shall  be  taken  at  a  distance  from  center  line  of  columns  equal  to 
/&(k  —  ?c)  +  %qc.  This  becomes  K(^2  +  c)  where  capital  is  circular.  For  slabs  having 
drop  panels  the  coefficient  of  Y±  should  be  used  instead  of  Jo- 

(h)  Arrangement  of  Reinforcement. — The  design  should  include  adequate  provision  for 
securing  the  reinforcement  in  place  so  as  to  take  not  only  the  maximum  moments  but  the 
moments  of  intermediate  sections.  If  bars  are  extended  beyond  the  column  capital  and 
are  used  to  take  the  bending  moment  on  the  opposite  side  of  the  column,  they  must 
extent  to  the  point  of  inflection.  Bars  in  diagonal  bands  used  as  reinforcement  for  negative 
moment  should  extend  on  each  side  of  the  line  drawn  through  the  column  center  at  right 
angles  to  the  direction  of  the  band  a  distance  equal  to  0.35  of  the  panel  length,  and  bars  in 
the  diagonal  bands  used  as  reinforcement  for  positive  moment,  should  extend  on  each  side 
of  the  diagonal  through  the  center  of  the  panel  a  distance  equal  to  0.35  of  the  panel  length. 
Bars  spliced  by  lapping  and  counted  as  only  one  bar  in  tension  shall  be  lapped  not  less  than 
80  diameters  if  splice  is  made  at  point  of  maximum  stress  and  not  more  than  50  per  cent 
of  the  rods  shall  be  so  spliced  at  any  point  in  any  single  band  or  in  any  single  region  of 
tensile  stress.  Continuous  bars  shall  not  all  be  bent  up  at  the  same  point  of  their  length, 
but  the  zone  in  which  this  bending  occurs  should  extend  on  each  side  of  the  assumed  point 
of  inflection. 

(i)  Tensile  and  Compressive  Stresses. — The  usual  method  of  calculating  the  tensile  and 
compressive  stresses  in  the  concrete  and  in  the  reinforcement,  based  on  the  assumptions 
for  internal  stresses,  should  be  followed.  In  the  case  of  the  drop  panel,  the  section  of  the 
slab  and  drop  panel  may  be  considered  to  act  integrally  for  a  width  equal  to  a  width  of  the 
column  head  section.  Within  the  column  head  section  the  allowable  compression  may  be 
increased  as  prescribed  in  Section  7  for  continuous  members. 

0')  Provision  for  Diagonal  Tension  and  Shear. — In  calculations  for  the  shearing  stress 
which  is  to  be  used  as  the  means  for  measuring  the  resistance  to  diagonal  tension  stress,  it 

262 


shall  be  assumed  that  the  total  vertical  shear  on  a  column  head  section  constituting  a 
width  equal  to  one-half  the  lateral  dimension  of  the  panel,  for  use  in  determining  critical 
shearing  stresses,  shall  be  considered  to  be  one-fourth  of  the  total  dead-  and  live-load  on  a 
panel  for  a  slab  of  uniform  thickness,  and  to  be  0.3  of  the  sum  of  the  dead-  and  live-loads  on 
a  panel  for  a  slab  with  drop  panels.^  The  formula  for  shearing  unit  stress  shall  be  v  = 
f\  *)  ^  TV  0^0  TV 

'     .     for  slabs  of  uniform  thickness  and  v  =    '     ,  -  for  slabs  with  drop  panels,  where  W  is 
bjd  bja 

the  sum  of  the  dead-  and  live-load  on  a  panel,  6  is  half  the  lateral  dimension  of  the  panel 
measured  from  center  to  center  of  columns,  and  jd  is  the  lever  arm  of  the  resisting  couple 
at  the  section. 

The  calculation  for  punching  shear  shall  be  made  on  the  assumption  of  a  uniform  distri- 
bution over  the  section  of  the  slab  around  the  periphery  of  the  column  capital  and  also  of  a 
uniform  distribution  over  the  section  of  the  slab  around  the  periphery  of  the  drop  panel, 
using  in  each  case  an  amount  of  vertical  shear  greater  by  25  per  cent  than  the  total  vertical 
shear  on  the  section  under  consideration. 

The  values  of  working  stresses  should  be  those  recommended  for  diagonal  tension  and 
shear  in  Section  10. 

(k)  Walls  and  Openings. — Additional  slab  thickness,  girders,  or  beams  shall  be  provided 
to  carry  walls  and  other  concentrated  loads  which  are  in  excess  of  the  working  capacity  of 
the  slab.  Beams  should  also  be  provided  in  case  openings  in  the  floor  reduce  the  working 
strength  of  the  slab  below  the  required  carrying  capacity.  Where  lintels  are  used  with 
flat-slab  construction  the  depth  of  the  lintels  being  greater  than  the  combined  depth  of 
the  slab  and  depressed  panel,  they  shall  be  designed  to  carry  a  uniformly  distributed 
load  equal  to  /-§  of  the  total  panel  load  in  addition  to  any  other  loads  superimposed  upon 
the  lintel  and  the  dead  weight  of  the  lintel. 

(1)  Unusual  Panels. — The  coefficients,  steel  distribution,  and  thicknesses  recommended 
are  for  slabs  which  have  three  or  more  rows  of  panels  in  each  direction  and  in  which  the 
sizes  of  the  panels  are  approximately  the  same.  For  structures  having  a  width  of  one  or 
two  panels,  and  also  for  slabs  having  panels  of  markedly  different  sizes,  an  analysis  should 
be  made  of  the  moments  developed  in  both  slab  and  columns  and  the  values  given  herein 
modified  accordingly. 

(m)  Oblong  Panels. — The  requirements  of  design  herein  given  for  flat-slab  floors  do  not 
apply  for  oblong  panels  where  the  long  side  is  more  than  four-thirds  of  the  short  side. 

(n)  Bending  Moments  in  Columns. — Provision  shall  be  made  in  both  wall  columns  and 
interior  columns  for  the  bending  moment  which  will  be  developed  by  unequally  loaded 
panels,  eccentric  loading,  or  uneven  spacing  of  columns.  The  amount  of  moment  to  be 
taken  by  a  column  will  depend  on  the  relative  stiffness  of  columns  and  slab,  and  computa- 
tions may  be  made  by  rational  methods  such  as  the  principle  of  least  work  or  of  slope  and 
deflection.  Generally  the  largest  part  of  the  unequalized  negative  moment  will  be  trans- 
mitted to  the  columns  and  the  columns  shall  be  designed  to  resist  this  bending  moment. 
Especial  attention  shall  be  given  to  wall  columns  and  corner  columns.  Column  capitals 
shall  be  designed,  and  reinforced  where  necessary,  with  these  conditions  in  mind. 

The  resistance  of  any  wall  column  to  bending  in  a  direction  perpendicular  to  the  wall 
shall  be  not  less  than  0.04  ivl\(li  —  gc)2  in  which  h  is  the  panel  dimension  perpendicular  to 
the  wall.  The  moment  in  such  wall  column  may  be  reduced  by  the  balancing  moment 
of  the  weight  of  the  structure  which  projects  beyond  the  center  line  of  the  supporting 
wall  column. 

Where  the  column  extends  through  the  story  above,  the  resisting  moment  shall  be 
divided  between  the  upper  and  the  lower  columns  in  proportion  to  their  stiffness.  Calcu- 
lated combined  stresses  due  to  bending  and  direct  load  shall  not  exceed  by  more  than  50 
per  cent  the  stresses  allowed  for  direct  load. 

13.  Columns — General. — Reinforced-concrete  columns,  for  the  working  stresses  here- 
inafter specified,  shall  have  a  gross  width  or  diameter  not  less  than  one-fifteenth  of  the 
unsupported  height  nor  less  than  twelve  (12)   in.     All  vertical   reinforcement  shall  be 
secured  against  lateral  displacement  by  steel  ties  not  less  than  j£  in.  in  diameter,  placed 
not  farther  apart  than  15  diameters  of  the  vertical  rods  or  more  than  12  in. 

For  columns  supporting  flat-slab  floors  or  roofs,  the  diameter  shall  be  not  less  than 
one-thirteenth  of  the  distance  between  columns. 

The  length  of  columns  shall  be  taken  as  the  maximum  unstayed  length. 

14.  Columns  with  Longitudinal  Reinforcement. — For  columns  having  not  less  than 
0.5  per  cent  nor  more  than  4  per  cent  of  vertical  reinforcement,  the  allowable  working  unit 
stress  for  the  net  section  of  the  concrete  shall  be  25  per  cent  of  the  compressive  strength 
specified  in  Section  6,  and  the  working  unit  stress  for  the  steel  shall  be  based  upon  the 
ratio  of  the  moduli  of  elasticity  of  the  concrete  and  steel.     Concrete  to  a  depth  of  1 3^  in. 
shall  be  considered  as  protective  covering  and  not  a  part  of  the  net  section. 

15.  Columns  with  Longitudinal  and  Lateral  Reinforcement. — Columns,  having  not  less 
than  1  per  cent  nor  more  than  4  per  cent  of  vertical  reinforcement  and  not  less  than  0.5  per 

263 


cent  nor  more  than  2  per  cent  of  lateral  reinforcement  in  the  form  of  hoops  or  spirals  spaced 
not  farther  apart  than  one-sixth  of  the  outside  diameter  of  the  hoops  or  spirals  nor  more 
than  3  in.  shall  have  an  allowable  working  unit  stress  for  the  concrete  within  the  outside 
diameter  of  the  hoops  or  spirals  equal  to  25  per  cent  of  the  compressive  strength  of  the 
concrete,  as  given  in  Section  6,  and  a  working  unit  stress  on  the  vertical  reinforcement  equal 
to  the  working  value  of  the  concrete  multiplied  by  the  ratio  of  the  specified  moduli  of 
elasticity  of  the  steel  and  concrete,  and  a  working  load  for  the  hoops  or  spirals  determined 
by  considering  the  steel  in  hoops  or  spirals  as  four  times  as  effective  as  longitudinal  rein- 
forcing steel  of  equal  volume.  The  percentage  of  lateral  reinforcement  shall  be  taken  as 
the  volume  of  the  hoops  or  spirals  divided  by  the  volume  of  the  enclosed  concrete  in  a  unit 
length  of  column.  The  hoops  or  spirals  shall  be  rigidly  secured  at  each  intersection  to  at 
least  four  (4)  verticals  to  insure  uniform  spacing.  The  percentage  of  longitudinal  reinforce- 
ment used  shall  be  not  less  than  the  percentage  of  the  lateral  reinforcement.  Spirals  shall 
be  manufactured  of  steel  having  a  yield  point  of  not  less  than  50,000  Ib.  per  square  inch. 

16.  For  steel  columns  filled  with  concrete  and  encased  in  a  shell  of  concrete  at  least 
3  in.  thick,  where  the  steel  is  calculated  to  carry  the  entire  load,  the  allowable  stress  per 

square  inch  shall  be  determined  by  the  following  formula:   18,000  —  70^,  but  shall  not 

exceed  16,000  Ib. — where  L  =  unsupported  length  in  inches  and  R  =  least  radius  of 
gyration  of  steel  section  in  inches.  The  concrete  shell  shall  be  reinforced  with  wire  mesh  or 
hoop  weighing  at  least  0.2  Ib.  per  square  foot  of  surface  of  shell. 

When  the  details  of  the  structural  steel  are  such  as  to  fully  enclose  or  encase  the  concrete, 
or  where  a  spiral  of  not  less  than  one-half  of  1  per  cent  of  the  core  area,  and  with  a  pitch  of 
not  more  than  3  in.,  is  provided  for  this  purpose,  the  concrete  inside  the  column  core 
or  spiral  may  be  loaded  to  not  more  than  25  per  cent  of  the  ultimate  strength  specified  in 
Section  6,  in  addition  to  the  load  on  the  steel  column  figured  as  above. 

Composite  columns  having  a  cast  iron  core  or  center  surrounded  by  concrete  which  is 
enclosed  in  a  spiral  of  not  less  than  one-half  of  1  per  cent  of  the  core  area,  and  with  a  pitch 
of  not  more  than  3  in.  may  be  figured  for  a  stress  of  12,000  —  60L/R,  but  not  over  10,000 
Ib.  per  square  inch  on  the  cast  iron  section  and  of  not  more  than  25  per  cent  of  the  com- 
pressive strength  specified  in  Section  6  on  the  concrete  within  the  spiral  or  core.  The 
diameter  of  the  cast  iron  core  shall  not  exceed  one-half  of  the  diameter  of  the  spiral. 

17.  Footings — General. — Symmetrical,  concentric  column  footings  shall  be  designed  for 
punching  shear,  diagonal  tension,  and  bending  moment. 

18.  Punching  Shear  in  Footings. — Punching  shear  shall  be  figured  in  accordance  with 
Section  10. 

19.  Diagonal  Tension  in  Footings. — Shearing  stresses  shall  be  figured  in  accordance 
with  Section  10. 

20.  Bending  Moment  in  Footings. — The  bending  moment  in  isolated  column  footings 
at  a  section  taken  at  edge  of  pier  or  column  shall  be  determined  by  multiplying  the  load  on 
the  quarter  footing  (after  deducting  the  quarter  pier  or  column  area)  by  six-tenths  of  the 
distance  from  the  edge  of  pier  or  column  to  the  edge  of  footing.     The  effective  area  of 
concrete  and  steel  to  resist  bending  moment  shall  be  considered  as  that  within  a  width 
extending  both  sides  of  pier  or  column,  a  distance  equal  to  depth  of  footing  plus  one-half 
the  remaining  distance  to  edge  of  footing,  except  that  reinforcing  steel  crossing  the  section 
other  than  at  right  angles,  shall  be  considered  to  have  an  effective  area  determined  by 
multiplying  the  section  area  by  the  line  of  the  angle  between  the  bar  and  the  plane   of 
section. 

21.  Bond  Stresses  in  Footings. — In  designing  footings,  careful  consideration  must  be 
given  to  the  bond  stresses  which  will  occur  between  the  reinforcing  steel  and  the  concrete. 

22.  Walls — General. — Walls  shall  be  reinforced  by  steel  rods  running  horizontally  and 
vertically.     Walls  having  an  unsupported  height  not  exceeding  fifteen  times  the  thickness 
may  be  figured  the  same  as  columns.     Walls  having  an  unsupported  height  not  more  than 
twenty-five  times  the  thickness  may  be  figured  to  carry  safely  a  working  stress  of  12%  per 
cent  of  the  compressive  strength  specified  in  Section  6. 

23.  Exterior  Walls. — Exterior  walls  shall  be  designed  to  withstand  wind  loads  or  loads 
from  backfill.     The  thickness  of  wall  shall  in  no  case  be  less  than  4  in. 

24.  Protection. — The   reinforcement   in   columns   and    girders   shall   be   protected   by 
minimum   thickness   of  2  in.  of  concrete;  in  beams  and  walls  by  a  minimum  of    lj^     in. 
in  floor  slabs  by  a  minimum  of  Y±  in. ;  in  footings  by  a  minimum  of  3  in. 


264 


NEW  YORK  BUILDING  CODE  REQUIREMENTS 

Working  Stresses. — Reinforced  concrete  structures  shall  be  so  designated  that  the 
stresses  in  pounds  per  square  inch  shall  not  exceed  the  following: 

Extreme  fibre  stress  on  concrete  in  compression 650 

Concrete  in  direct  compression 500 

Shearing  stress  in  concrete  when  all  diagonal  tension  is  resisted  by 

steel 150 

Shearing  stress  in  concrete  when  diagonal  tension  is  not  resisted  by 

steel 40 

Bond  stress  between  concrete  and  plain  reinforcement 80 

Bond  stress  between  concrete  and  approved  deformed  bars 100 

Tensile  stress  in  steel  reinforcement 16,000 

Tensile  stress  in  cold  drawn  steel  wire  or  fabric,  35  per  cent  of  the 

elastic  limit  but  not  more  than 20,000 

In  continuous  beams  the  extreme  fiber  stress  on  concrete  in  compression  may  be  in- 
creased 15  per  cent,  adjacent  to  supports. 

The  ratio  of  the  moduli  of  elasticity  of  1  :  2  :  4  stone  or  gravel  concrete  and  steel  shall  be 
taken  as  one  to  fifteen.  The  ratio  of  the  moduli  of  elasticity  of  1  :  1^  :  3  stone  or  gravel 
concrete  and  steel  shall  be  taken  'as  one  to  twelve. 

Slabs  and  Beams,  (a)  Thickness. — Slabs  shall  not  be  less  than  4  in.  in  thickness  for 
floors  and  3%  in.  for  roofs. 

(b)  Tee-Beams. — Where  adequate  bond  between  slab  and  web  of  beam  is  provided,  the 
slab  may  be  considered  as  an  integral  part  of  the  beam  provided  its  effective  width  shall 
not  exceed  on  either  side  of  the  beam  one-sixth  of  the  span  length  of  the  beam,  nor  be 
greater  than  six  times  the  thickness  of  the  slab  on  either  side  of  the  beam,  the  measure- 
ments being  taken  from  edge  of  web. 

(c)  Placing  of  Reinforcement. — All  reinforcement  shall  be  accurately  located  and  secured 
against  displacement.     The  reinforcement  for  slabs  shall  not  be  spaced  farther  apart  than 
two  and  one- half  times  the 'thickness  of  the  slab. 

(d)  Web  Reinforcement. — Members  of  web  reinforcement  shall  be  so  designed  as  ade- 
quately to  take  up  throughout  their  length  all  stresses  not  taken  up  by  the  concrete.     They 
shall  not  be  spaced  to  exceed  three-fourths  of  the  depth  of  the  beam  in  that  portion  where 
the  web  stresses  exceed  the  allowable  value  of  concrete  in  shear.     Web  reinforcement, 
unless  rigidly  attached,  shall  be  placed  at  right  angles  to  the  axis  of  the  beam  and  carried 
around  the  tension  members.     •    • 

Use  of  Fillers  in  Floor  Construction. — When  hollow  tile,  concrete  blocks  or  other 
acceptable  fillers  are  used  in  any  reinforced  concrete  floor  construction,  the  reinforced  con- 
crete members  of  such  floor  construction  shall  be  designed  in  accordance  with  the  provisions 
of  this  article  to  take  the  entire  loads,  provided,  however,  that  when  the  fillers  do  not  exceed 
60  per  cent  of  the  construction,  not  more  than  2^  in.  of  concrete  shall  be  required  over 
the  fillers. 

Columns,  (a)  With  Longitudinal  Reinforcements  Only. — In  concrete  columns,  having 
not  less  than  one-half  nor  more  than  4  per  cent  of  vertical  reinforcement  secured  against 
displacement  by  24-in.  steel  ties  placed  not  farther  apart  than  15  diameters  of  the  verti- 
cal rods  nor  more  than  12  in.,  the  allowable  load  shall  be  500  lb.  per  square  inch  on  the 
concrete,  plus  7,500  lb.  on  the  vertical  reinforcement. 

(6)  With  Longitudinal  and  Lateral  Reinforcement. — In  concrete  columns,  having  not  less 
than  one-half  nor  more  than  2  per  cent  of  hoops  or  spirals  spaced  not  farther  apart  than 
one-sixth  of  the  diameter  of  the  enclosed  column  nor  more  than  3  in.,  and  having  not  less 
than  1  nor  more  than  4  per  cent  of  vertical  reinforcement,  the  allowable  load  shall  be  500 
lb.  per  square  inch  on  the  effective  area  of  the  concrete,  plus  7,500  lb.  per  square  inch  on 
the  vertical  reinforcement,  plus  a  load  per  square  inch  on  the  effective  area  of  the  concrete 
equal  to  two  times  the  percentage  of  lateral  reinforcement  multiplied  by  the  tensile  stress  in 
the  lateral  reinforcement  prescribed  under  "  Working  Stresses,"  the  percentage  of  lateral 
reinforcement  being  the  volume  of  the  hoops  or  spirals  divided  by  the  volume  of  the  en- 

265 


closed  concrete  in  a  unit  length  of   column.     The  hoops  or  spirals  shall  be  rigidly  secured 
to  at  least  four  verticals  to  insure  uniform  spacing. 

(c)  Structural  Steel  and  Concrete. — In  columns  of  structural  steel,  thoroughly  encased  in 
concrete  not  less  than  4  in.  thick  and  reinforced  with  not  less  than  1  per  cent  of  steel,  the 
allowable  load  shall  be  16,000  lb.  per  square  inch  on  the  structural  steel,  the  percentage  of 
reinforcement  being  the  volume  of  the  reinforcing  steel  divided  by  the  volume  of  the  con- 
crete enclosed  by  the  reinforcing  steel.     Not  more  than  one-half  of  the  reinforcing  steel 
shall  be  placed  vertically.     The  reinforcing  steel  shall  not  be  placed  nearer  than  1  in.  to 
the  structural  steel  or  to  the  outer  surface  of  the  concrete.    The  ratio\>f  length  to  least  radius 
of  gyration  of  structural  steel  section  shall  not  exceed  one  hundred  and  twenty. 

(d)  When  Richer  Concrete  is  Used. — In  concrete  columns  the  compression  on  the  concrete 
may  be  increased  20  per  cent  when  the  fine  and  coarse  aggregates  are  carefully  selected 
and  the  proportion  of  cement  to  total  aggregate  is  increased  to  one  part  of  cement  to  not 
more  than  four  and  one-half  parts  of  aggregate,  fine  and  coarse,  either  in  the  proportion 
of  one  part  of  cement,  one  and  one-half  parts  of  fine  aggregate  and  three  parts  of  coarse 
aggregate*,  or  in  such  proportion  as  will  secure  the  maximum  density.     In  such  cases, 
however,  the  compressive  stress  in  the  vertical  steel  shall  not  exceed  7,200  lb.  per  square 
inch. 

(e)  Eccentric  Loads. — Bending  stresses  due  to  eccentric  loads  shall  be  provided  for  by 
increasing  the  section  of  concrete  or  steel  until  the  maximum  stress  shall  not  exceed  the 
allowable  working  stress. 

(/)  Length. — In  columns,  the  ratio  of  length  to  least  side  or  diameter  shall  not  exceed 
fifteen,  but  in  no  case  shall  the  least  side  or  diameter  be  less  than  12  in. 

Walls. — Enclosure  walls  of  reinforced  concrete  shall  be  securely  anchored  at  all  floors. 
The  thickness  shall  not  be  less  than  one-twenty-fifth  of  the  unsupported  height,  but  in  no 
case  less  than  8  in.  The  steel  reinforcement,  running  both  horizontally  and  vertically, 
shall  be  placed  near  both  faces  of  the  wall;  the  total  weight  of  such  reinforcement  shall  be 
not  less  than  }4,  lb.  per  square  foot  of  wall. 

Protection  of  Reinforcement. — The  reinforcement  in  columns  and  girders  shall  be 
protected  by  a  minimum  of  2  in.  of  concrete;  in  beams  and  walls  by  a  minimum  of  1^  in.; 
in  floor  slabs  by  a  minimum  of  1  in.;  and  in  footings  by  a  minimum  of  4  in.  of  concrete. 

Flat  Slabs* 

Application. — The  rules  governing  the  design  of  reinforced  concrete  flat  slabs  shall  apply 
to  such  floors  and  roofs,  consisting  of  three  or  more  rows  of  slabs,  without  beams  or  girders, 
supported  on  columns,  the  construction  being  continuous  over  the  columns  and  forming 
with  them  a  monolithic  structure. 

Compliance  with  Building  Code. — In  the  design  of  reinforced  concrete  flat  slabs,  the 
provisions  of  the  preceding  articles  of  the  building  code  shall  govern  with  respect  to  such 
matters  as  are  specified  therein. 

Assumptions. — In  calculations  for  the  strength  of  reinforced  concrete  flat  slabs,  the 
following  assumptions  shall  be  made: 

(a)  A  plane  section  before  bending  remains  plane  after  bending. 

(6)  The  modulus  of  elasticity  of  concrete  in  compression  within  the  allowable  working 
stresses  is  constant. 

(c)  The  adhesion  between  concrete  and  reinforcement  is  perfect. 

(d)  The  tensile  strength  of  concrete  is  nil. 

(e)  Initial  stress  in  the  reinforcement  due  to  contraction  or  expansion  in  the  concrete  is 
negligible. 

Stresses. — (a)  The  allowable  unit  shear  in  reinforced  concrete  flat  slabs  on  the  bd 
section  around  the  perimeter  of  the  column  capital  shall  not  exceed  120  lb.  per  square  inch; 
and  the  allowable  unit  shearing  stress  on  the  bjd  section  around  the  perimeter  of  the  drop 
shall  not  exceed  (60)  lb.  per  square  inch,  provided  that  the  reinforcement  is  so  arranged  or 
anchored  that  the  stress  may  be  fully  developed  for  both  positive  and  negative  moments. 

The  extreme  fibre  stresses  to  be  used  in  concrete  in  compression  at  the  column  head 
section  shall  not  exceed  750  lb.  per  square  inch. 

Columns. — For  columns  supporting  reinforced  concrete  flat  slabs,  the  least  dimension  of 
any  column  shall  be  not  less  than  one-fifteenth  of  the  average  span  of  any  slabs  supported 
by  the  columns;  but  in  no  case  shall  such  least  dimension  of  any  interior  column  supporting 
a  floor  or  roof  be  less  than  16  in.  when  round,  nor  14  in.  when  square;  nor  shall  the  least 
dimension  of  any  exterior  column  be  less  than  14  in. 

Column  Capital. — Every  reinforced  concrete  column  supporting  a  flat  slab  shall  be 
provided  with  a  capital  whose  diameter  is  not  less  than  0.225  of  the  average  span  of  any 
slabs  supported  by  it.  Such  diameter  shall  be  measured  where  the  vertical  thickness  of  the 
capital  is  at  least  1^  in.,  and  shall  be  the  diameter  of  the  inscribed  circle  in  that  horizontal 

*  Adopted  July  8,  1920. 

266 


plane.  The  slope  of  the  capital  considered  effective  below  the  point  where  its  diameter  is 
measured  shall  nowhere  make  an  angle  with  vertical  of  more  than  45°.  In  case  a  cap  of  less 
dimensions  than  hereinafter  described  as  a  drop,  is  placed  above  the  column  capital,  the 
part  of  this  cap  enclosed  within  the  lines  of  the  column  capital  extended  upwards  to  the 
bottom  of  the  slab  or  drop  at  the  slope  of  45°  may  be  considered  as  part  of  the  column 
capital  in  determining  the  diameter  for  design  purposes. 

Drop. — When  a  reinforced  concrete  flat  slab  is  thicker  in  that  portion  adjacent  to  or 
surrounding  the  column,  the  thickened  portion  shall  be  known  as  a  drop.  The  width  of 
such  drop  when  used,  shall  be  determined  by  the  shearing  stress  in  the  slab  around  the 
perimeter  of  the  drop,  but  in  no  case  shall  the  width  be  less  than  0.33  of  the  average  span  of 
any  slabs  of  which  it  forms  a  part.  In  computing  the  thickness  of  drop  required  by  the 
negative  moment  on  the  column  head  section,  the  width  of  the  drop  only  shall  be  considered 
as  effective  in  resisting  the  compressive  stress,  but  in  no  case  shall  the  thickness  of  such 
drops  be  less  than  0.33  of  the  thickness  of  the  slab.  Where  drops  are  used  over  interior 
columns,  corresponding  drops  shall  be  employed  over  exterior  columns  and  shall  extend  to 
the  one-sixth  point  of  panel  from  the  center  of  the  column. 

Slab  Thickness. — The  thickness  of  a  reinforced  concrete  flat  slab  shall  be  not  less  than 
that  derived  by  the  formulae  t  =  0.024Z/\/w  +  I'M  f°r  slabs  without  drops,  and  t  =  0.02 
L\A0  +  1  for  slabs  with  drops,  in  which  t  is  the  thickness  of  the  slab  in  inches,  L  is  the 
average  span  of  the  slab  in  feet,  and  w  is  the  total  live-  and  dead-load  in  pounds  per  square 
foot;  but  in  no  case  shall  this  thickness  be  less  than  one-thirty-second  of  the  average  span 
of  the  slab  for  floors,  nor  less  than  one-fortieth  of  the  average  span  of  the  slab  for  roofs,  nor 
less  than  6  in.  for  floors  nor  less  than  5  in.  for  roofs. 

Reinforcement. — (a)  In  the  calculation  of  moments  at  any  section,  all  the  reinforcing 
bars  which  cross  that  section  may  be  used,  provided  that  such  bars  extend  far  enough 
on  each  side  of  such  section  to  develop  the  full  amount  of  the  stress  at  that  section.  The 
effective  area  of  the  reinforcement  at  any  moment  section  shall  be  the  sectional  area  of  the 
bars  crossing  such  section  multiplied  by  the  sine  of  the  angle  of  such  bars  with  the  plane  of 
the  section.  The  distribution  of  the  reinforcement  of  the  several  bands  shall  be  arranged  to 
fully  provide  for  the  intermediate  moments  at  any  section. 

(fe)  Splices  in  bars  may  be  made  wherever  convenient  but  preferably  at  points  of  mini- 
mum stress.  The  length  of  any  splice  shall  be  not  less  than  80  bar  diameters  and  in  no  case 
less  than  2  ft.  The  splicing  of  adjacent  bars  shall  be  avoided  as  far  as  possible.  Slab  bars 
which  are  lapped  over  the  column,  the  sectional  area  of  both  being  included  in  the  calcula- 
tion for  negative  moment,  shall  extend  to  the  lines  of  inflection  beyond  the  column  center. 

(c)  When  the  reinforcement  is  arranged  in  bands,  at  least  50  per  cent  of  the  bars  in  any 
band  shall  be  of  a  length  not  less  than  the  distance  center  to  center  of  columns  measured 
rectangularly  and  diagonally;  no  bars  used  as  positive  reinforcement  shall  be  of  a  length  less 
than  half  the  panel  length  plus  40  bar  diameters  for  cross  bands,  or  less  than  seven-tenths 
of  the  panel  length  plus  40  bar  diameters  for  diagonal  bands  and  no  bars  used  as  negative 
reinforcement  shall  be  of  a  length  less  than  half  the  panel  length.  All  reinforcement 
framing  perpendicular  to  the  wall  in  exterior  panels  shall  extend  to  the  outer  edge  of  the 
panel  and  shall  be  hooked  or  otherwise  anchored. 

(d~)  Adequate  means  shall  be  provided  for  properly  maintaining  all  slab  reinforcement  in 
the  position  assumed  by  the  computations. 

Line  of  Inflection. — In  the  design  of  reinforced  concrete  flat  slab  construction,  for  the 
purpose  of  making  calculations  of  the  bending  moments  at  sections  other  than  defined  in 
these  rules,  the  line  of  inflection  shall  be  considered  as  being  located  one-quarter  the 
distance,  center  to  center,  of  columns,  rectangularly  and  diagonally,  from  center  of  columns 
for  panels  without  drops,  and  three-tenths  of  such  distance  for  panels  with  drops. 

Moment  Sections. — For  the  purpose  of  design  of  reinforced  concrete  flat  slabs,  that 
portion  of  the  section  across  a  panel,  along  a  line  midway  between  columns,  which  lies 
within  the  middle  two  quarters  of  the  width  of  the  panel  shall  be  known  as  the  inner  section, 
and  those  portions  of  the  section  in  the  two  outer  quarters  of  the  width  of  the  panel  shall  be 
known  as  the  outer  sections.  Of  the  section  which  follows  a  panel  edge  from  column  to 
column  and  which  includes  the  quarter  perimeters  of  the  edges  of  the  column  capitals,  that 
portion  within  the  middle  two  quarters  of  the  panel  width  shall  be  known  as  the  mid  section 
and  the  two  remaining  portions,  each  having  a  projected  width  equal  to  one-quarter  of  the 
panel  width  shall  be  known  as  the  column  head  sections. 

Bending  Moments. — In  the  design  of  reinforced  concrete  flat  slabs  the  following  provi- 
sions with  respect  to  bending  moments  shall  be  observed.  In  the  moment  expressions 
used: 

W  is  the  total  dead-  and  live-load  on  the  panel  under  consideration,  including  the  weight 
of  drop  whether  a  square,  rectangle  or  parallelogram. 

Wi  is  the  total  live-load  on  the  panel  under  consideration. 

L  is  the  length  of  side  of  a  square  panel  center  to  center  of  columns;  or  the  average  span 
of  a  rectangular  panel  which  is  the  mean  length  of  the  two  sides. 

267 


n  is  the  ratio  of  the  greater  to  the  less  dimension  of  the  panel. 

h  is  the  unsupported  length  of  a  column  in  inches,  measured  from  top  of  slab  to  base  of 
capital. 

/  is  the  moment  of  inertia  of  the  reinforced  concrete  column  section. 

A.  Interior  Square  Panels. — The  numerical  sum  of  the  positive  and  negative  moments 
shall  be  not  less  than  Y\  7  WL.     A  variation  of  plus  or  minus  5  per  cent  shall  be  permitted 
in  the  expression  for  the  moment  on  any  section,  but  in  no  case  shall  the  sum  of  the  negative 
moments  be  less  than  66  per  cent  of  the  total  moment,  nor  the  sum  of  the  positive  moments 
be  less  than  34  per  cent  of  the  total  moment  for  slabs  with  drops;  nor  shall  the  sum  of  the 
negative  moments  be  less  than  60  per  cent  of  the  total  moment,  nor  the  sum  of  the  positive 
moments  be  less  than  40  per  cent  of  the  total  moment  for  slabs  without  drops. 

In  two-way  systems,  for  slabs  with  drops,  the  negative  moment  resisted  on  two  column 
head  sections  shall  be—^2^L;  the  negative  moment  on  the  mid  section  shall  be—  Ms3 
WL;  the  positive  moment  on  the  two  outer  sections  shall  be  +  %oWL  and  the  positive 
moment  on  the  inner  section  shall  be  +  Mss^FL;  and  for  slabs  without  drops,  the  negative 
moment  resisted  on  two  column  head  sections  shall  be  —%sWL,  the  negative  moment  on 
the  mid  section  shall  be— ^33  WL,  the  positive  moment  on  the  two  outer  sections  shall 
be  +  }^^WL  and  the  positive  moment  on  the  inner  section  shall  be  +  M.ssWL, 

In  four- way  systems,  the  negative  moments  shall  be  as  specified  for  two-way  systems; 
the  positive  moment  on  Ijie  two  outer  sections  shall  be  +  HooWL,  and  the  positive 
moment  on  the  inner  section  shall  be  +  ^looWL  for  slab  with  drops;  and  the  positive 
moment  on  the  two  outer  sections  shall  be  +  ^j.^WL,  and  the  positive  moment  on  the 
inner  section  shall  be  +  ^ooWL,  for  slabs  without  drops. 

In  three-way  systems,  the  negative  moment  on  the  column  head  and  mid  sections  and 
the  positive  moment  on  the  two  outer  sections,  shall  be  as  specified  for  four-way  systems. 
In  the  expression  for  the  bending  moments  on  the  various  sections,  the  length  L  shall  be 
assumed  as  the  distance  center  to  center  of  columns,  and  the  load  W  as  the  load  on  the 
panel  parallelogram. 

B.  Interior  Rectangular  Panels. — When  the  ratio  n  does  not  exceed  1.1,  all  computa- 
tions shall  be  based  on  a  square  panel  of  a  length  equal  to  the  average  span,  and  the  rein- 
forcement shall  be  equally  distributed  in  the  short  and  long  directions  according  to  the 
bending  moment  coefficients  specified  for  interior  square  panels. 

When  the  ratio  n  lies  between  1.1  and  1.33,  the  bending  moment  coefficients  specified 
for  interior  square  panels  shall  be  applied  in  the  following  manner: 

(a)  In  two-way  systems,  the  negative  moments  on  the  two  column  head  sections  and  the 
mid  section  and  the  positive  moment  on  the  two  outer  sections  and  the  inner  section  at  right 
angles  to  the  long  direction  shall  be  determined  as  for  a  square  panel  of  a  length  equal  to  the 
greater  dimension  of  the  rectangular  panel;  and  the  corresponding  moments  on  the  sections 
at  right  angles  to  the  short  direction  shall  be  determined  as  for  a  square  panel  of  a  length 
equal  to  the  lesser  dimension  of  the  rectangular  panel.  In  no  case  shall  the  amount  of 
reinforcement  in  the  short  direction  be  less  than  two-thirds  of  that  in  the  long  direction. 
The  load  W  shall  be  taken  as  the  load  on  the  rectangular  panel  under  consideration. 

(6)  In  four-way  systems,  for  the  rectangular  bands,  the  negative  moment  on  the  column 
head  sections  and  the  positive  moment  on  the  outer  sections  shall  be  determined  in  the  same 
manner  as  indicated  for  the  two-way  systems. 

For  the  diagonal  bands,  the  negative  moments  on  the  column  head  and  mid  sections  and 
the  positive  moment  on  the  inner  section  shall  be  determined  as  for  a  square  panel  of  a  length 
equal  to  the  average  span  of  the  rectangle.  The  load  W  shall  be  taken  as  the  load  on  the 
rectangular  panel  under  consideration. 

(c)  In  three-way  systems,  the  negative  and  positive  moments  on  the  bands  running 
parallel  to  the  long  direction  shall  be  determined  as  for  a  square  whose  side  is  equal  to 
the  greater  dimension;  and  the  moments  on  the  bands  running  parallel  to  the  short  direc- 
tion shall  be  determined  as  for  a  square  whose  side  is  equal  to  the  lesser  dimension.  The 
load  W  shall  be  taken  as  the  load  on  the  parallelogram  panel  under  consideration. 

C.  Exterior  Panels. — The  negative  moments  at  the  first  interior  row  of  columns  and 
the  positive  moments  at  the  center  of  the  exterior  panels  on  moment  sections  parallel  to 
the  wall,  shall  be  increased  20  per  cent  over  those  specified  above  for  interior  panels. 
The  negative  moment  on  moment  sections  at  the  wall  and  parallel  thereto  shall  be  deter- 
mined by  the  conditions  of  restraint,  but  the  negative  moment  on  the  mid  section  shall 
never  be  considered  less  than  50  per  cent  and  the  negative  moment  on  the  column  head 
section  never  less  than  80  per  cent  of  the  corresponding  moments  at  the  first  interior  row  of 
columns. 

D.  Interior    columns  shall  be  designed  for  the  bending  moments  developed  by  un- 
equally loaded  panels,   eccentric  loading  or  uneven  spacing  of  columns.     The  bending 
moment  resulting  from  unequally  loaded  panels  shall  be  considered  as  Y±§W\L,  and  shall 
be  resisted  by  the  columns  immediately  above  and  below  the  floor  line  under  consideration 
in  direct  proportion  to  the  values  of  their  ratios  of  I /h. 

E.  Wall  columns  shall  be  designed  to  resist  bending  in  the  same  manner  as  interior 

268 


columns,  except  that  W  shall  be  substituted  for  Wi  in  the  formula  for  the  moment.  The 
moment  so  computed  may  be  reduced  by  the  counter  moment  of  the  weight  of  the  structure 
which  projects  beyond  the  center  line  of  the  wall  columns. 

F.  Roof  columns  shall  be  designed  to  resist  the  total  moment  resulting  from  unequally 
loaded  panels,  as  expressed  by  the  formulae  in  paragraphs  (D)  and  (E)  of  this  rule. 

Walls  and  Openings. — In  the 'design  and  construction  of  reinforced  concrete  flat  slabs, 
additional  slab  thickness,  girders  or  beams  shall  be  provided  to  carry  any  walls  or  concen- 
trated loads  in  addition  to  the  specified  uniform  live-  and  dead-loads.  Such  girders  or 
beams  shall  be  assumed  to  carry  20  per  cent  of  the  total  live  and  dead  panel  load  in  addition 
to  the  wall  load.  Beams  shall  also  be  provided  in  case  openings  in  the  floor  reduce  the 
working  strength  of  the  slab  below  the  presciibed  carrying  capacity. 

Special  Panels. — For  structures  having  a  width  of  less  than  three  rows  of  slabs,  or  in 
which  exterior  drops,  capitals  or  columns  are  omitted,  or  in  which  irregular  or  special 
panels  are  used,  and  for  which  the  rules  relating  to  the  design  of  reinforced  flat  slabs  do 
not  directly  apply,  the  computations  in  the  analysis  of  the  design  of  such  panels,  shall, 
when  so  required,  be  filed  with  the  superintendent  of  buildings. 


269 


CHICAGO  BUILDING  CODE  REQUIREMENTS 

Ratio  of  Moduli  of  Elasticity — Adhesion — Bond,  (a)  The  calculations  for  the  strength 
of  reinforced  concrete  shall  be  based  on  the  assumed  ultimate  compressive  strength  per 
square  inch  designated  by  the  letter  "  C7"  given  in  the  table  below  for  the  mixture  to  be 
used. 

(b)  The  ratio  designated  by  the  letter  "#"  of  the  modulus  of  elasticity  of  steel  to  that 
of  the  different  grades  of  concrete  shall  be  taken  in  accordance  with  the  following  table: 

Mixture  U  R 

cement,  1  sand,  2  broken  stone,  gravel  or  slag 2,900  10 

cement,  1%  sand,  3  broken  stone,  gravel  or  slag 2,400  12 

cement,  2  sand,  4  broken  stone,  gravel  or  slag 2,000  15 

cement,  2^  sand,  5  broken  stone,  gravel  or  slag 1,750  18 

cement,  3  sand,  7  broken  stone,  gravel  or  slag 1,500  20 

Unit  Stresses  for  Steel  and  Concrete,  (a)  The  stresses  in  the  concrete  and  the  steel 
shall  not  exceed  the  following  limits: 

(6)  Tensile  stress  in  steel  shall  not  exceed  one-third  of  its  elastic  limits  and  shall  not 
exceed  18,000  Ib.  per  square  inch. 

(c)  Shearing  stress  in  steel  shall  not  exceed  12,000  Ib.  per  square  inch. 

(d)  The  compressive  stress  in  steel  shall  not  exceed  the  product  of  the  compressive 
stress  in  the  concrete  multiplied  by  the  elastic  modulus  of  the  steel  and  divided  by  the 
elastic  modulus  of  the  concrete. 

(e)  Direct  compression  in  concrete  shall  be  one-fifth  of  its  ultimate  strength.     Bending 
in  extreme  fiber  of  concrete  shall  be  thirty-five  one-hundredths  of  the  ultimate  strength. 

(/)  Tension  in  concrete  on  diagonal  plane  shall  be  one-fiftieth  of  the  ultimate  compres- 
sive strength. 

((/)  For  a  concrete  composed  of  one  part  of  cement,  two  parts  of  sand  and  four  parts  of 
broken  stone,  the  allowable  unit  stress  for  adhesion  per  square  inch  of  surface  of  imbedment 
shall  not  exceed  the  following: 

Pounds  per 
sq.  in. 

On  plain  round  or  square  bars  of  structural  steel 70 

On  plain  round  or  square  bars  of  high  carbon  steel 50 

On  plain  flat  bars  in  which  the  ratio  of  the  sides  is  not  more  than  2  to  1 .  .        50 
On  twisted  bars  when  the  twisting  is  not  less  than  one  complete  twist  in 
8  diameters 100 

(h)  For  specially  formed  bars,  the  allowable  unit  stress  for  bond  shall  not  exceed  one- 
fourth  of  the  ultimate  bond  strength  of  such  bars  without  appreciable  slip  which  shall 
be  determined  by  tests  made  by  the  person,  firm  or  corporation  to  the  satisfaction  of  the 
Commissioner  of  Buildings,  but  provided  that  in  no  case  shall  such  allowable  unit  stress 
exceed  100  Ib.  per  square  inch  of  the  specially  formed  bars. 

Design  for  Slabs,  Beams  and  Girders. — Reinforced  concrete  slabs,  beams  and  girders 
shall  be  designed  in  accordance  with  the  following  assumptions  and  requirements. 

(a)  The  common  theory  of  flexure  shall  be  applied  to  beams  and  members    resisting 
bending. 

(b)  The  adhesion  between  the  concrete  and  the  steel  shall  be  sufficient  to  make  the  two 
materials  act  together. 

(c)  The  steel  to  take  all  the  direct  tensile  stresses. 

(d)  The  stress  strain  curve  of  concrete  in  compression  is  a  straight  line. 

(e)  The  ratio  of  the  moduli  of  elasticity  of  concrete  to  steel  shall  be  as  specified  in  the 
table  in  preceding  article. 

Moments  of  External  Forces,  (a)  Beams,  girders,  floor  or  roof  slabs  and  joists  shall  be 
calculated  as  supported,  or  with  fixed  ends,  or  with  partly  fixed  ends,  in  accordance  with  the 
actual  end  conditions,  the  number  of  spans  and  the  design. 

(b)  When  calculated  for  ends  partly  fixed  for  intermediate  spans  with  an  equally  distri- 
buted load  where  the  adjacent  spans  are  of  approximately  equal  lengths: 

270 


Bending  moment  at  center  of  spans  shall  not  be  less  than  that  expressed  in  the  formula 
-TO~  for  intermediate  spans  and  -^  for  end  spans. 

WL* 

(c)  The  moment  over  supports  shall  not  be  less  than  the  formula  —  =-  and  the  sum  of 

lo 

the  moments  over  one  support  and  at  the  center  of  span  shall  be  taken  not  less  than  the 

.     WL* 
formula  —  5— 
o 

In  the  formula  hereinabove  given  "TF"  is  the  load  per  lineal  foot  and  "L"  the  length 
of  span  in  feet. 

(d)  In  case  of  concentrated  or  special  loads  the  calculations  shall  be  based  on  the  critical 
condition  of  loading. 

(e)  For  fully  supported  slabs,  the  free  opening  plus  the  depth,  for  continuous  slabs,  the 
distance  between  centers  of  supports,  is  to  be  taken  as  the  span. 

(/)  Where  the  vertical  shear,  measured  on  the  section  of  a  beam  or  girder  between  the 
centers  of  action  of  the  horizontal  stresses,  exceeds  one-fiftieth  of  the  ultimate  direct 
compressive  stress  per  square  inch,  web  reinforcement  shall  be  supplied  sufficient  to  carry 
the  excess.  The  web  reinforcement  shall  extend  from  top  to  bottom  of  beam,  and  loop  or 
connect  to  the  horizontal  reinforcement.  The  horizontal  reinforcement  carrying  the  direct 
stresses  shall  not  be  considered  as  web  reinforcement. 

(0)  In  no  case,  however,  shall  the  vertical  shear,  measured  as  stated  above,  exceed  one- 
fifteenth  of  the  ultimate  compression  strength  of  the  concrete. 

(h)  For  T-beams  the  width  of  the  stem  only  shall  be  used  in  calculating  the  above  shear. 

(t)  When  steel  is  used  in  the  compression  side  of  beams  and  girders,  the  rods  shall  be  tied 
in  accordance  with-  requirements  of  vertical  reinforced  columns  with  stirrups  connecting 
with  the  tension  rods  of  the  beams  or  girders. 

0')  All  reinforcing  steel  shall  be  accurately  located  in  the  forms  and  secured  against 
displacement;  and  inspected  by  the  representative  of  the  architect  or  engineer  in  charge 
before  any  surrounding  concrete  be  put  in  place.  It  shall  be  afterwards  completely  in- 
closed by  the  concrete,  and  such  steel  shall  nowhere  be  nearer  the  surface  of  the  concrete 
than  \}^  inches  for  columns,  lj^  inches  for  beams  and  girders,  and  }£  inch,  but  not  less 
than  the  diameter  of  the  bar,  for  slabs. 

(fc)  The  longitudinal  steel  in  beams  and  girders  shall  be  so  disposed  that  there  shall  be  a 
a  thickness  of  concrete  between  the  separate  pieces  of  steel  of  not  less  than  one  and  one-half 
times  the  maximum  sectional  dimension  of  the  steel. 

(1)  For  square  slabs  with  two-way  reinforcements  the  bending  moment  at  the  center  of 

WL2 
the  slab  shall  be  not  less  than  that  expressed  in  the  formula  -(>-.~  for  intermediate  spans,  and 


. 

tor  end  spans. 

W7.2 

(ra)  The  moment  over  supports  shall  not  be  less  than  the  formula  -^-  and  the  sum  of 

OO 

the  moments  over  one  support  and  at  the  center  of  the  span  shall  be  taken  not  less  than  the 

WL* 
formula  -TO-- 

In  which  above  formula  "  TF"  is  the  load  per  lineal  foot  and  "L"  the  length  of  the  span. 

(n)  For  square  or  rectangular  slabs,  the  distribution  of  the  loads  in  the  two  directions, 
shall  be  inversely  as  the  cubes  of  the  two  dimensions. 

(o)  Exposed  metal  of  any  kind  will  not  be  considered  a  factor  in  the  strength  of  any  part 
of  any  concrete  structure,  and  the  plaster  finish  applied  over  the  metal  shall  not  be  deemed 
sufficient  protection  unless  applied  of  sufficient  thickness  and  so  secured  as  to  meet  the 
approval  of  the  Commissioner  of  Buildings. 

(p)  Shrinkage  and  thermal  stresses  shall  be  provided  for  by  introduction  of  steel. 

Limiting  Width  of  Flange  in  "T"  Beams.  —  (a)  In  the  calculation  of  ribs,  a  portion  of 
the  floor  slab  may  be  assumed  as  acting  in  flexure  in  combination  with  the  rib.  The  width 
of  the  slab  so  acting  in  flexure  is  to  be  governed  by  the  shearing  resistance  between  rib  and 
slab,  but  limited  to  a  width  equal  to  one-third  of  the  span  length  of  the  ribs  between  sup- 
ports and  also  limited  to  a  width  of  three-quarters  of  the  distance  from  center  to  center 
between  ribs. 

(6)  No  part  of  the  slab  shall  be  considered  as  a  portion  of  the  rib,  unless  the  slab  and 
rib  are  cast  at  the  same  time. 

(c)  Where  reinforced  concrete  girders  support  reinforced  concrete  beams,  the  portion  of 
floor  slab  acting  as  flange  to  the  girder  must  be  reinforced  with  rods  near  the  top,  at  right 
angles  to  the  girder,  to  enable  it  to  transmit  local  loads  directly  to  the  girder  and  not  through 
the  beams. 

Reinforced  Concrete  Columns  —  Limit  of  Length  —  Per  cent  of  Reinforcement  —  Bending 
Moment  in  Columns  —  Tying  Vertical  Rods.  —  (a)  Reinforced  concrete  may  be  used  for 

271 


columns  in  which  the  concrete  shall  not  be  leaner  than  a  1:2:4  mixture  and  in  which  the 
ratio  of  length  to  least  side  or  diameter  does  not  exceed  twelve,  but  in  no  case  shall  the 
cross  section  of  the  column  be  less  than  64  sq.  in.  Longitudinal  reinforcing  rods 
must  be  tied  together  to  effectively  resist  outward  flexure  at  intervals  of  not  more  than 
twelve  times  least  diameter  of  rod  and  not  more  than  18  in.  When  compression 
rods  are  not  required,  reinforcing  rods  shall  be  used,  equivalent  to  not  less  than  one-half  of 
1  per  cent  (0.005)  of  the  cross  sectional  area  of  the  column;  provided,  however,  that  the 
total  sectional  area  of  the  reinforcing  steel  shall  not  be  less  than  1  sq.  in.,  and  that 
no  rod  or  bar  be  of  smaller  diameter  or  least  dimensions  than  /^-in.  The  area  of  rein- 
forcing compression  rods  shall  be  limited  to  3  per  cent  of  cross  sectional  area  of  the 
column.  Vertical  reinforcing  rods  shall  extend  upward  or  downward  into  the  column, 
above  or  below,  lapping  the  reinforcement  above  or  below  enough  to  develop  the  stress  in 
rod  by  the  allowable  unit  for  adhesion.  When  beams  or  girders  are  made  monolithic  with 
or  rigidly  attached  to  reinforced  concrete  columns,  the  latter  shall  be  designed  to  resist  a 
bending  moment  equal  to  the  greatest  possible  unbalanced  moment  in  the  beams  or  girders 
at  the  columns,  in  addition  to  the  direct  loads  for  which  the  columns  are  designed. 

(6)  When  the  reinforcement  consists  of  vertical  bars  and  spiral  hooping,  the  concrete  may 
be  stressed  to  one-fourth  of  its  ultimate  strength  as  given  on  page  270,  provided,  that  the 
amount  of  vertical  reinforcement  be  not  less  than  the  amount  of  the  spiral  reinforcement, 
nor  greater  than  8  per  cent  of  the  area  within  the  hooping;  that  the  percentage  of  spiral 
hooping  be  not  less  than  one-half  of  1  per  cent  nor  greater  than  1.5  per  cent;  that  the 
pitch  of  the  spiral  hooping  be  uniform  and  not  greater  than  one-tenth  of  the  diameter 
of  the  column,  nor  greater  than  3  in.;  that  the  spiral  be  secured  to  the  verticals  at  every 
intersection  in  such  a  manner  as  to  insure  the  maintaining  of  its  form  and  position,  that 
the  verticals  be  spaced  so  that  their  distance  apart,  measured  on  the  circumference  be 
not  greater  than  9  in.,  nor  one-eighth  the  circumference  of  the  column  within  the 
hooping.  In  such  columns,  the  action  of  the  hooping  may  be  assumed  to  increase  the 
resistance  of  the  concrete  equivalent  to  two  and  one-half  times  the  amount  of  the  spiral 
hooping  figured  as  vertical  reinforcement.  No  part  of  the  concrete  outside  of  the  hooping 
shall  be  considered  as  a  part  of  the  effective  column  section. 

Structural  Steel  Columns. — When  the  vertical  reinforcement  consists  of  a  structural 
steel  column  of  box  shape,  with  lattice  or  batten  plates  of  such  a  form  as  to  permit  its  being 
filled  with  concrete,  the  concrete  may  be  stressed  to  one-fourth  of  its  ultimate  strength  as 
given  in  table  on  page  270,  provided  that  no  shape  of  less  than  1  sq.  in.  section  be 
used  and  that  the  spacing  of  the  lacing  or  battens  be  not  greater  than  the  least  width  of  the 
columns. 

Curtain  Walls  in  Skeleton  Construction  Buildings. — Buildings  having  a  complete 
skeleton  construction  of  steel  or  of  reinforced  concrete  construction,  or  a  combination  of 
both,  may  have  exterior  walls  of  reinforced  concrete  8  in.  thick;  provided,  however, 
that  such  walls  shall  support  only  their  own  weight  and  that  such  walls  shall  have  steel 
reinforcement  of  not  less  -than  three-tenths  of  1  per  cent  in  each  direction,  vertically  and 
horizontally,  the  rods  spaced  not  more  than  12-in.  centers  and  wired  to  each  other  at 
each  intersection.  All  bars  shall  be  lapped  for  a  length  sufficient  to  develop  their  full 
stress  for  the  allowable  unit  stress  for  adhesion.  Additional  bars  shall  be  set  around  open- 
ings, the  verticals  wired  to  the  nearest  horizontal  bars,  and  the  horizontal  bars  at  top  and 
bottom  of  openings  shall  be  wired  to  the  nearest  vertical  bars.  The  steel  rods  shall  be 
combined  with  the  concrete  and  placed  where  the  combination  will  develop  the  greatest 
strength,  and  the  rods  shall  be  staggered  or  placed  and  secured  so  as  to  resist  a  pressure  of 
30  Ib.  per  square  foot,  either  from  the  exterior  or  from  the  interior  on  each  and  every 
square  foot  of  each  wall  panel. 

Flat  Slabs* 

1.  Definitions. — Flat  slabs  as  understood  by  this  ruling  are  reinforced  concrete  slabs, 
supported  directly  on  reinforced  columns  with  or  without  plates  or  capitals  at  the  top,    the 
whole  construction  being  hingeless  and  monolithic  without  any  visible  beams  or  girders. 
The  construction  may  be  such  as  to  admit  the  use  of  hollow  panels  in  the  ceiling  or  smooth 
ceiling  with  depressed  panels  in  the  floor. 

2.  The  column  capital  shall  be  defined  as  the  gradual  flaring  out  of  the  top  of  the  column 
without  any  marked  offset. 

3.  The  drop  panel  shall  be  defined  as  a  square  or  rectangular  depression  around   the 
column  capital  extending  below  the  slab  adjacent  to  it. 

4.  The  panel  length  shall  be  defined  as  the  distance  c.  to  c.  of  columns  of  the  side  of  a 
square  panel,  or  the  average  distance  c.  to  c.  of  columns  of  the  long  and  short  sides  of  a 
rectangular  panel. 

5.  Columns. — The  least  dimension  of  any  concrete  column  shall  be  not  less  than    one- 
twelfth  the  panel  length,  nor  one-twelfth  the  clear  height  of  the  column. 

*  Went  into  effect  Mar.  1,  1918. 

272 


6.  Slab  Thickness.— The  minimum  total  thickness  of  the  slab  in  inches  shall  be  deter- 
mined by  the  formula:  t  =  W     /44(  =  square  root  of  W  divided  by  44),  where  t  =  total 
thickness  of  slab  in  inches,  W  =  total  live-load  and  dead-load  in  pounds  on  the  panel, 
measured  c.  to  c.  of  columns. 

7.  In  no  case  shall  the  thickness  be  less  than  >^2  of  the  panel  length  (L/32)  for  floors, 
nor  VIQ  of  the  panel  length  (Z//40)  for  roofs  (L  being  the  distance  c.  to  c.  of  columns). 

8.  In  no  case  shall  the  thickness  of  slab  be  less  than  6  in.  for  floors  or  roofs. 

9.  Column  Capital. — When  used  the  diameter  of  the  column  capital  shall  be  measured 
where  its  vertical  thickness  is  at  least  1)^  in.  and  shall  be  at  least  0.225  of  the  panel  length. 

The  slope  of  the  column  capital  shall  nowhere  make  an  angle  with  the  vertical  of  more 
than  45  deg.  Special  attention  shall  be  given  to  the  design  of  the  column  capital  in  con- 
sidering eccentric  loads,  and  the  effect  of  wind  upon  the  structure. 

10.  Drop  Panel. — When  used,  the  drop  panel  shall  be  square  or  circular  for  square 
panels  and  rectangular  or  elliptical  for  oblong  panels. 

11.  The  length  of  the  drop  shall  not  be  less  than  one-third  of  the  panel  length  (Z//3) 
if  square,  and  not  less  than  one-third  of  the  long  or  short  side  of  the  panel  respectively,  if 
rectangular. 

12.  The  depth  of  the  drop  panel  shall  be  determined  by  computing  it  as  a  beam,  using 
the  negative  moment  over  the  column  capital  specified  elsewhere  in  this  ruling. 

13.  In  no  case,  however,  shall  the  dimensions  of  the  drop  panel  be  less  than  required  for 
punching  shear  along  its  perimeter,  using  the  allowable  unit  shearing  stresses  specified  below. 

14.  Shearing  Stresses. — The  allowable  unit  punching  shear  on  the  perimeter  of  the 
column  capital  shall  be  ^oo  °f  the  ultimate  compressive  strength  of  the  concrete  as  given 
on  page  270.     The  allowable  unit  shear  on  the  perimeter  of  the  drop  panel  shall  be  0.03 
of  the  ultimate  compressive  strength  of  the  concrete.     In  computing  shearing  stress  for 
the  purpose  of  determining  the  resistance  to  diagonal  tension  the  method  specified  by  the 
ordinance  shall  be  used. 

15.  Panel   Strips. — For  the  purpose  of  establishing  the   bending  moments  and    the 
resisting  moments  of  a  square  panel,  the  panel  shall  be  divided  into  strips  known  as  strip 
A  and  strip  B.     Strip  A  shall  include  the  reinforcement  and  slab  in  a  width  extending  from 
the   center  line  of  the  columns  for  a  distance  each  side  of  this  center  line  equal  to  one- 
quarter  of  the  panel  length.     Strip  B  shall  include  the  reinforcement  and  slab  in  the  half 
width  remaining  in  the  center  of  the  panel.     At  right  angles  to  these  strips,  the  panel  shall 
lie  divided  into  similar  strips  A  and  B,  having  the  same  widths  and  relations  to  the  center 
line  of  the  columns  as  the  above  strips.     These  strips  shall  be  for  designing  purposes  only, 
and  are  not  intended  as  the  boundary  lines  of  any  bands  of  steel  used. 

16.  These  strips  shall  apply  to  the  system  of  reinforcement  in  which  the  reinforcing  bars 
are  placed  parallel  and  at  right  angles  to  the  center  line  of  the  columns,  hereinafter  known 
as  the  two-way  system,  and  also  to  the  system  of  reinforcement  in  which  the  reinforcing 
bars  are  placed  parallel,  at  right  angles  to  and  diagonal  to  the  center  line  of  the  columns 
hereinafter  known  as  the  four-way  system. 

17.  Any  other  system  of  reinforcement  in  which  the  reinforcing  bars  are  placed  in  cir- 
cular, concentric  rings  and  radial  bars,  or  systems  with  steel  rods  arranged  in  any  manner 
whatsoever,  shall   comply  with  the   requirements  of  either  the  two-way  or  the  four-way  . 
system  herein  specified. 

18.  Bending  Moment  Coefficients,  Interior  Panel,  Two-way  System. — In  panels  where 
standard  drops  and  column  capitals  are  used  as  above  specified,  the  negative  bending 
moment,  taken  at  a  cross-section  of  each  strip  A  at  the  edge  of  the  column  capital  or  over 
it,  shall  be  taken  as  TTL/30. 

19.  The  positive  bending  moment  taken  at  a  cross-section  of  each  strip  A  midway 
between  column  centers  shall  be  taken  as  WL/60. 

20.  The  positive  bending  moment  taken  at  a  cross-section  of  each  strip  B  in  the  middle 
of  the  panel  shall  be  taken  as  WL/12Q. 

21.  The  negative  bending  moment  taken  at  a  cross-section  of  each  strip  B  on  the  center 
line  of  the  columns  shall  be  taken  as  WL/12Q. 

22.  In  the  formulas  hereinabove  given  W  =  total  live-  and  dead-load  on  the  whole  panel 
in  pounds,  L  =  panel  length,  c.  to  c.  of  columns. 

23.  Bending  Moment  Coefficients,  Interior  Panel,  Four-way  System. — In  panels  where 
standard  drops  and  column  capitals  are  used  as  above  specified,  the  negative  bending 
moment,  taken  at  a  cross-section  of  each  strip  A  at  the  edge  of  column  capital  or  over  it, 
shall  be  taken  as  WL/30. 

24.  The  positive  bending  moment,  taken  at  a  cross-section  of  each  strip  A,  midway 
between  column  centers,  shall  be  taken  as  WL/8O. 

25.  The  positive  bending  moment,  taken  at  a  cross-section  of  each  strip  B,  taken  in  the 
middle  of  the  panel,  shall  be  taken  as  TFL/120. 

26.  The  negative  bending  moment,  taken  at  a  cross-section  of  each  strip  B  on  the  center 
line  of  the  columns,  shall  be  taken  as  JFL/120. 

273 


27.  Bending  Moment  Coefficients,  Wall  Panels. — Where  wall  panels  with  standard 
drops  and  capitals  are  carried  by  columns  and  girders  built  in  walls,  as  in  skeleton  con- 
struction, the  same  coefficients  shall  be  used  as  for  an  interior  panel,  except  as  follows: 
The  positive  bending  moments  on  strips  A  and  B  midway  between  wall  and  first  line  of 
columns  shall  be  increased  25  per  cent. 

28.  Where  wall  panels  are  carried  on  new  brick  walls,  these  shall  be  laid  in  Portland 
cement  mortar  and  shall  be  stiffened  with  pilasters  as  follows:  If  a  16-in.  wall  is  used,  it 
shall  have  a  4-in.  pilaster.     If  a  12-in.  wall  is  used,  it  shall  have  an  8-in.  pilaster.     The  length 
of  pilasters  shall  be  not  less  than  the  diameter  of  the  column,  nor  less  than  one-eighth  of 
the  distance  between  pilasters.     The  pilasters  shall  be  located  opposite  the  columns  as 
nearly  as  practicable,  and  shall  be  corbeled  out  4  in.  at  the  top,  starting  at  the  level  of  the 
base  of  the  column  capital.     Not  less  than  8-in.  bearing  shall  be  provided  for  the  slab,  the 
full  length  of  wall. 

The  coefficients  of  bending  moments  required  for  these  panels  shall  be  the  same  as  those 
for  the  interior  panels  except  as  provided  herewith:  The  positive  bending  moments  on 
strips  A  and  B  midway  between  the  wall  and  first  line  of  columns  shall  be  increased  50 
per  cent. 

29.  Where  wall  panels  are  supported  on  old  brick  walls,  there  shall  be  columns   with 
standard  drops  and  capitals  built  against  the  wall,  which  shall  be  tied  to  the  same  in  an 
approved  manner,  and  at  least  an  8-in.  bearing  provided  for  the  slab,  the  full  length. 
Where  this  is  impracticable,  there  shall  be  built  a  beam  on  the  underside  of  slab  adjacent  to 
the  wall  between  columns,  strong  enough  to  carry  25  per  cent  of  the  panel  load. 

The  coefficients  of  bending  moments  for  the  two  cases  of  slab  support  herein  described 
shall  be  the  same  as  those  specified  in  Sect.  27  and  Sect.  28  for  skeleton  and  wall  bearing 
condition,  respectively. 

30.  Nothing  specified   above  shall  be  construed  as  applying  to  a  case  of  slabs  merely 
resting  on  walls  or  ledges,  without  any  condition  of  restraint.     These  shall  be  figured  as  in 
ordinary  beam-and-girder  construction  specified  in  the  ordinances. 

31.  Bending   Moment   Coefficients,   Wall   and  Interior   Columns. — Wall   columns    in 
skeleton  construction  shall  be  designed  to  resist  a  bending  moment  of  TFL/60  at  floors  and 
TFL/30  at  roof.     The  amount  ot  steel  required  for  this  moment  shall  be  independent 
of    that    required    to    carry   the   direct  load.     It  shall   be   placed   as   near  the   surfaces 
of    the     column    as    practicable    on    the    tension    sides,    and    the    rods    shall    be    con- 
tinuous in  crossing  from  one  side  to  another.     The  length  of  rods  below  the  base  of  the 
capital  and  above  the  floor  line  shall  be  sufficient  to  develop  their  strength  through  bond, 
but  not  less  than  40  diameters,  nor  less  than  one-third  the  clear  height  between  the  floor 
line  and  the  base  of  the  column  capital. 

32.  The  interior  columns   must  be  analyzed  for  the  worst  condition  of  unbalanced 
loading.     It  is  the  intention  of  this  ruling  to  cover  ordinary  cases  of  eccentric  loads  on  the 
columns  by  the  requirement  of  Sect.   5.     WThere   the   minimum  size  of  column  therein 
specified  is  found  insufficient,  however,  the  effect  of  the  resulting  bending  moment  shall 
be  properly  divided  between  the  adjoining  slab  and  the  columns  above  and  below  according 
to  best  principles  of  engineering,  and  the  columns  enlarged  sufficiently  to  carry  the  load 
safely. 

33.  Bending  Moment  Coefficients,  Panels  Without  Drops,  or  Capitals,  or  Both. — In 
square  panels  where  no  column  capital  or  no  depressions  are  used,  the  sum  total  of  positive 
and  negative  bending  moments  shall  be  equal  to  that  computed  by  the  following  formula: 

B.M.  =  (TFL/8)(1.53  -  4k  +  4.18A;3) 

where  B.M .  =  numerical  sum  of  positive  and  negative  bending  moments,   regardless  of 

algebraic  signs. 

W  =  total  live-  and  dead-load  on  the  whole  panel. 
L  =  length  of  side  of  a  square  panel,  c.  to  c.  of  columns. 
k  =  ratio  of  the  radius  of  the  column  or  column  capital  to  panel  length,  L. 

This  total  bending  moment  shall  be  divided  between  the  positive  and  the  negative 
moments  in  the  same  proportion  as  in  the  typical  square  panels  for  two-way  or  four-way 
systems  specified  above  for  interior  and  wall  panels  respectively. 

34.  Point  of  Inflection. — For  the  purpose  of  making  the  calculations  of  the  bending 
moment  at  the  sections  away  from  the  column  capital,  the  point  of  inflection  shall  be 
considered   as   being   one-quarter   the  distance  c.   to  c.  of  columns,   both  crosswise  and 
diagonally,  from  the  center  of  the  column. 

35.  Tensile  Stress  in  Steel  and  Compressive  Stress  in  Concrete. — The  tensile  stress  in 
steel  and  the  compressive  stress  in  the  concrete  to  resist  the  bending  moment  shall    be 
calculated  on  the  basis  of  the  reinforcement  and  slab  in  the  width  included  in  a  given  strip, 
and  according  to  the  assumptions  and  requirements  given  in  the  first  three  articles  on 

274 


page  270.     The  steel  shall  be  considered  as  being  concentrated  at  the  center  of  gravity  of 
all  the  bands  of  steel  in  a  given  strip. 

36.  For  the  four-way  system  of  reinforcement  the  amount  of  steel  to  resist  the  negative 
bending  moment  over  the  support  in  each  strip  A  shall  be  taken  as  the  sum  of  the  areas  of 
steel  in  one  cross  band  and  one  diagonal  band.     The  amount  of  steel  to  resist  the  positive 
bending  moment  of  each  strip  B  shall  be  considered  as  the  area  of  the  steel  in  a  diagonal 
band.     The  amount  of  steel  to  resist  the  positive  bending  moment  in  each  strip  A  shall 
be  considered  as  the  area  of  the  steel  in  a  cross  band,  and  the  amount  of  steel  to  resist 
the  negative  moment  in  each  strip  B  shall  be  the  steel  included  in  the  width  of  strip  B. 

37.  For  the  two-way  system  of  reinforcement  the  amount  of  steel  to  resist  the  bending 
moment  in  any  strip  shall  be  considered  as  the  area  of  steel  included  in  the  width  of  the 
strip. 

38.  In  both  systems  of  reinforcement  the  compressive  stress  in  the  concrete  in  any 
strip  shall  be  calculated  by  taking  the  area  of  steel  considered  for  each  strip  and  applying 
it  in  a  beam  formula  based  on  the  principles  given  in  the  article  on  "Design  for  Slabs, 
Beams  and  Girders"  on  page  270. 

39.  Where  drop  panels  are  used,  the  width  of  beam  assumed  to  resist  the  compressive 
stresses  over  the  column  capital  shall  be  the  width  of  the  drop. 

40.  The  width  of  beam,  where  no  drop  panels  are  used,  shall  be  the  width  of  steel  bands. 
Where  this  is  found  insufficient,  the  area  shall  be  increased  by  introducing   compression 
steel  in  the  bottom  of  slab. 

41.  Rectangular  Panels. — When  the  length  of  panel  in  either  two-way  or    four-way 
system  does  not  exceed  the  breadth  by  more  than  5  per  cent,  all  computations  shall  be 
based  on  a  square  panel  whose  side  equals  the  mean  of  the  length  and  breadth,  and  the 
steel   equally  distributed  among  the  strips  according  to  the  coefficients  above  specified. 

42.  In  no  rectangular  panel  shall  the  length  exceed  the  breadth  by  more  than  one-third 
of  the  latter. 

43.  Rectangular  Panels,  Four-way  System. — In  the  four-way  system  of  reinforcement, 
where  length  exceeds  breadth  by  more  than  5  per  cent,  the  amount  of  steel  required  in  strip 
A,  long  direction,  both  positive  and  negative,  shall  be  the  same  as  that  required  for  the 
same  strip  in  a  square  panel  whose  length  is  equal  to  the  long  side  of  the  rectangular  panel. 

44.  The  amount  of  steel,  strip  A,  short  direction,  positive  and  negative,  shall  be  the 
same  as  that  required  for  the  same  strip  in  a  square  panel,  whose  length  is  equal  to  the 
short  side  of  the  rectangular  panel. 

45.  The  amount  of  steel  in  strip  B,  positive  and  negative,  shall  be  the  same  as  that 
required  for  similar  strip  in  a  square  panel  whose  length  is  equal  to  the  mean  of  the  long 
and  the  short  side  of  the  rectangular  panel. 

46.  In  no  case  shall  the  amount  of  steel  in  the  short  side  be  less  than  two-thirds  of  that 
required  for  the  long  side. 

47.  Rectangular  Panels,  Two-way  System. — In  the  two-way  system  of  reinforcement 
the  amount  of  steel  required  for  the  positive  and  the  negative  moment  of  each  strip  A  shall 
be  determined  in  the  same  manner  as  indicated  for  the  four-way  system  above. 

48.  The  amount  of  steel  in  strip  B,  positive  and  negative,  running  in   short    direction, 
shall  be  equal  to  that  required  for  the  same  strip  in  a  square  panel  whose  length  equals  the 
long  side  of  the  rectangular  panel. 

49.  The  amount  of  steel  in  strip  B,  long  direction,  positive  and  negative,  shall  be  equal 
to  that  required  for  the  same  strip  in  a  square  panel,  whose  length  equals  the  short  side  of 
the  rectangular  panel. 

50.  In  no  case  shall  the  amount  of  steel  in  strip  B,  long  direction,  be  less  than  two-thirds 
of  that  in  the  short  direction. 

51.  Walls  and  Openings. — Girders  and  beams  shall  be  constructed  under  walls,  around 
openings  and  to  carry  concentrated  loads. 

52.  Spandrel  Beams. — The  spandrel  beams  or  girders  shall,  in  addition  to  their  own 
weight  and  the  weight  of  the  spandrel  wall,  be  assumed  to  carry  20  per  cent  of  the  wall 
panel  load  uniformly  distributed  upon  them. 

53.  Placing  of  Steel. — In  order  that  the  slab  bars  shall  be  maintained  in  the  position 
shown  in  the  design  during  the  work  of  pouring  the  slab,  spacers  and  supports  shall    be 
provided  satisfactory  to  the  Commissioner  of  Buildings.     All  bars  shall  be  secured  in  place 
at  intersections  by  wire  or  other  metal  fastenings.     In  no  case  shall  the  spacing  of  the  bars 
exceed  9  in.     The  steel  to  resist  the  negative  moment  in  each  strip  B  shall   extend   one- 
quarter  of  the  panel  length  beyond  the  center  line  of  the  columns  in  both  directions. 

54.  Splices  in  bars  may  be  made  wherever  convenient,  but  preferably  at  points  of 
minimum  stress.     The  length  of  splice  beyond  the  center  point,  in  each  direction,  shall  not 
be  less  than  40  diameters  of  the  bars,  nor  less  than  2  ft.     The  splicing  of  adjacent  bars  shall 
be  avoided  as  far  as  possible. 

55.  Slab  bars  which  are  lapped  over  the  column,  the  sectional  area  of  both   being  in- 
cluded in  the  calculations  for  negative  moment,  shall  extend  not  less  than  0.25  of  the  panel 
length  for  cross  bands  and  0.35  of  the  panel  length  for  diagonal  bands,  beyond  the  column 
center. 

275 


56.  Computations. — Complete  computations  of  interior  and  wall  panels  and  such  other 
portions  of  the  building  as  may  be  required  by  the  Commissioner  of  Buildings  shall  be 
left  in  the  office  of  the  Commissioner  of  Buildings  when  plans  are  presented  for  approval. 

57.  Test  of  Workmanship. — The  Commissioner  of  Buildings  or  his  representative  may 
choose  any  two  adjacent  panels  in  the  building  for  the  purpose  of  ascertaining  the  character 
of  workmanship.     The  test  shall  not  be  made  sooner  than  the  time  required  for  the  cement 
to  set  thoroughly,  nor  less  than  6  weeks  after  the  concrete  had  been  poured. 

58.  All  deflections  under  test  load  shall  be  taken  at  the  center  of  the  slab,  and  shall  be 
measured  from  the  normal  unloaded  position  of  the  slab.     The  two  panels  selected  shall  be 
uniformly  loaded  over  their  entire  area  with  a  load  equal  to  the  dead-load  plus  twice  the 
live-load,  thus  obtaining  twice  the  total  design  load.     The  load  shall  remain  in  place  not 
less  than  24  hr.     If  the  total  deflection  in  the  center  of  the  panel  under  the  test  load  does 
not  exceed  3^  o  0  °f  the  panel  length,  the  slab  may  be  placarded  to  carry  the  full  design  live- 
load.     If  it  exceeds  this  amount  of  deflection,  and  recovers  not  less  than  80  per  cent  of  the 
total  deflection  within  7  days  after  the  load  is  removed,  the  slab  may  be  placarded  to  carry 
the  full  design  live-load.     If  the  deflection  exceeds  the  allowable  amount  above  specified, 
and  the  recovery  is  less  than  80  per  cent  in  7  days  after  the  removal  of  the  test  load,  other 
tests  shall  be  made  on  the  same  or  other  panels,  the  results  of  which  will  determine  the 
amount  of  live-load  the  slabs  will  be  permitted  to  carry. 

59.  General. — The  design  and  the  execution  of  the  work  shall  conform  to  the  general 
provisions  and  the  spirit  of  the  Chicago  Building  Ordinances  in  points  not  covered  by  this 
Ruling  and  to  the  best  engineering  practice  in  general. 


276 


r.N 


OK  IS  DUE  ON  THE  LAST  DA1 
STAMPED  BELOW 

AN  INITIAL  FINE  OP  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


.... 

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APR    18  1943 

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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


